The known bugs page was formerly hosted here and has since been moved to the MASS software documentation site:

Known Bugs in MASS

For questions about specific bugs, or to report a bug, contact mass@canadamasonrycentre.com

When software bugs are found, notifications are posted in the Known Bugs page, on the MASS welcome screen, as well as here on the CMDC website software blog in an effort to be transparent and keep all MASS users informed. This issue was found within our own office as a result of some unrelated testing on Multi-storey walls in MASS Version 4.0. As a result, the fix will be incorporated into the next software release and in the meantime, must be checked for manually by engineers who may encounter this issue.

This post outlines the conditions required to trigger this error, where the design results could have been affected, the details of the bug itself, and how to check to see if this bug is present in any MASS project.

Jump straight to:

• • Bug Summary
  • Background Information
  • What types of designs might be affected?
  • How to check if a design is affected
  • Example
  • Our Response

Bug Summary

For shear wall element designs where the web grouting pattern has not been set to “fully grouted” and the flange is fully grouted as a result of vertical reinforcement placed in each cell, the maximum allowable axial load limit is overestimated. The actual envelope curve where axial load is considered to determine moment resistance is plotted correctly and not affected by this bug. As this upper portion of the diagram tends to also correspond to lower factored bending moments, designs with any significant lateral loading would also be unlikely to be affected by this particular item of concern.

The horizontal line represents the maximum axial load, P_r, and in designs affected by the bug, that line’s location is calculated by MASS to be higher than what it should be.

Since this is only triggered for fully grouted walls with the partial grouted selection, there may be other reasons why a bar is being placed in every cell beyond needing the moment resistance. For more information regarding why MASS may be placing so much steel, click here to open this related article (opens in a new tab).

Background Information

The MASS Software has a dedicated design routine for determining Pr,max. The maximum allowable is specified by CSA S304-14: 10.4.1 is 80% of the axial load corresponding to the assemblage in full compression (where ß₁c = l_w).

This upper limit is calculated using a dedicated process which uses a particular formula based on whether the wall is hollow, fully grouted, or somewhere in between. This is done individually for the shear wall web and each flange (or boundary element in the upcoming Version 4.0 release) where the total upper limit is equal to the sum of each of the components added up.

The actual values used in MASS can be found by scrolling down the Detailed Moment Results tab, shown below:

Excerpt from the Results tab showing Pr,max components

The 1039.6 kN value seen in MASS has been incorrectly calculated using the f’_{m,hollow, flange} = 10 PMa instead of the correct f’_m,eff,flange = 7.5 MPa.

Once P_r,max has been calculated, it is can be seen on the P-M diagram (also referred to as the interaction diagram) near the top where a horizontal line is plotted. Values capped by P_r,max as well as those which extend further upward are both shown and can be selected by the user to see more exact values of the individual points.

Pro Tip: When a point is selected, the arrow keys can be used to jump to adjacent points along the envelope curve.

The actual values used along the interaction diagram curve are correctly plotted and are unaffected by this bug. This issue is specifically the height at which the upper limit on axial load has been capped.

What types of designs might be affected?

In order to have a design result that was declared by MASS to be successful when it should not have been, there are two conditions that would have to occur:

Condition 1: The cross section and input selections would need to trigger the bug in the P_r,max calculation.

This means that shear wall flanges with the “partially grouted” selection applied with bars placed in each cell as a result of other user input values are the only types of designs that can have the incorrect P_r,max value calculated. If any one of these conditions is not met, the correct maximum axial load is calculated and even for affected cross sections where the bug is present, the plotted P-M Diagram envelope is still correct, with the exception of the height at which it is capped. Click here to jump to a full description of how to verify this condition

Condition 2: The loading needs to result in an axial factored load that exceeds what would have been the correct P_r,max value.

Load combinations with relatively low factored moments coupled with high axial loads may lie between P_r,max shown in MASS and the correct value. Click here to jump to the full description of how this can be checked in any MASS project file.

Each of these conditions is elaborated upon in the subsequent sections below. If unsure whether a previous design performed in MASS has been affected, MASS technical support is available to manually check the detailed results and confirm whether or not this bug is present in any project file.

How to tell if a design has been affected

Often times, this bug can be seen at a glance by viewing the P-M Diagram for any design. If the horizontal line drawn at P_r,max does not appear to be roughly 80% between the origin and the location where the envelope meets the vertical axis, this project file may be affected. This check is broken down into two conditions, both of which must be satisfied for a design’s results to have been impacted by this bug.

Any use of the software results for design, as well as checks, calculations, and verification described in this section and elsewhere is done at the sole discretion of the user using their own professional judgment. If you have any questions and are not 100% confident in your understanding of the material, please contact MASS support for further assistance.

Manually checking P_r,max (Condition 1)

Confirming whether this bug is present in any MASS project file is a fairly simple procedure. The most thorough approach is to manually calculate the flange contribution to P_r,max seen in the Detailed Moment Results (see example further below for demonstration), however, this can also be done by viewing the P-M Diagram drawing and locating the point of pure compression along the outer envelope curve.

Note: For shear wall designs with flanges, this will correspond to a neutral axis location of the total wall length (including flange thicknesses) divided by 0.8. Also known as the highest point with a corresponding moment resistance of zero.

Visual Inspection Method

In many cases, this issue can be identified by simply eyeballing the general height of the P_r,max limit and comparing it to where roughly 80% or 4/5ths of the height should be capped for the design. The figure below shows an example P-M diagram on the left where the bug is present and from visual inspection alone is clearly not capped at the correct height. The corresponding diagram for the same cross section is shown on the right with the flange grouting pattern changed from “Partially grouted” to “Fully grouted” and as a result, the bug is no longer present and it can be seen that the maximum axial load is capped at the correct height.

Another option is to click on the very top point on the diagram which lies on the P_f axis and multiple that by 0.80. This is less exact than verifying the calculation using the correct inputs (described further below) but can still get a result accurate to within 20kN which will be acceptable for the majority of cases.

Extreme cases like this are relatively easy to spot with a quick glance of the P-M Diagram. The example used in this article is outlined further below, here, and was purposely done using very long flanges and low masonry unit strength to highlight this issue. It is possible that this difference is less pronounced and is less obvious.

That being said, just because the bug is present in a project file does not necessarily mean that there are any issues with the design results.

Checking Load Combination Locations on the P-M Diagram (Condition 2)

If there is an issue with the incorrect P_r,max value being used, simply check the P-M Diagram and click on the load combinations with the highest factored axial load, P_f.

Any load combination can be selected in MASS by clicking on the point to reveal the exact factored moment, moment resistance, factored axial load, and neutral axis location.

The factored axial load, or P_f , can be compared to the correct P_r,max value to ensure that even if a shear wall’s envelope has not been capped at the correct location, it is still within the acceptable range.

Quick Calculation Check by Hand

If loads are in the upper region of the diagram and the P_r,max line appears roughly in the correct location, it is a good idea to quickly check the numbers by hand. This situation is covered in the section below. In the Detailed Moment Results section of the software where the P_r,max equations and formulas are found, the results can be quickly verified make sure they are correct.

Note: the f’_m value used in the P_r,max calculation can be found in the Detailed Shear Wall Properties section of the results window, along with all of the other inputs.

If any value of P_f exceeds P_r,max that was calculated manually in the subsection above, MASS has incorrectly passed these designs when they should have failed. If unsure, please do not hesitate to contact MASS support.

Example Design

To illustrate this example, a test case was chosen with many aspects that amplify this error. Consider a basic shear wall design where the web is 2210 mm long (2190 mm plus a 10 mm mortar joint on each end) with a height of 3400 mm and a total height of 24,000 mm. Disable masonry unit selections until only the 15 cm, 15 MPa unit are remaining.

Note: for typical design work, it is generally recommended to first leave several options selected before seeing an initial result and narrowing down the design from there. For purposes of demonstrating this bug, this example involves an already known cross section which is the reason for the other options being disabled.

Once the web design has been specified, click on the flange input tab and add a 2000 mm long flange to each end of the wall. Using the default offset value, specify the distance from the critical section to the top of the web as the total height value used earlier: 24,000 mm. This is a commonly missed step which will ensure that a portion of each flange is included in the cross section used for design. If this value were left at the default 0 mm, only the portions of the flanges directly adjacent to the web (140 mm in this case) would actually be used.

Once the flanges have been specified, click on the loads button and enter basically anything. In this example, a 1kN lateral dead load is applied simply to allow the MASS software to advance to the moment design stage. Since this bug relates to the envelope curve, exact loading is irrelevant as it only impacts where the load combination points will be drawn on the diagram.

Upon running a moment design, there should be successful results displayed with a fairly large spacing of vertical bars. Click on the PM Diagram drawing and note the location of the Pr,max line where axial load is capped.

So far in this example, the bug has not yet presented itself. Proceed by disabling all of the spacings except for 200mm, placing a vertical bar in every cell. It is these designs where you may notice a dramatic shift in Pr,max.

Breaking down the calculation of Pr,max, it is made up of three components: the left flange, the web, and the right flange. Selecting the Detailed Moment Results tab, these values can be seen in the results screen, as well as below:

Manually checking these flange values based on the inputs seen, the following is the expected (and correct) value:

Referring back to the bug summary, this issue presents itself when a shear wall web becomes fully grouted due to a vertical bar placed in every cell at 200mm spacing. The f’_m value used for the flanges is incorrect, referencing the hollow value of 10Mpa instead of the grouted 7.5MPa from Table 4.

As mentioned at the start of this subsection, the example chosen for this demonstration exercise for a few reasons. The first is that a small, low strength masonry unit was chosen because in percentage terms, there is a very large jump (33%) going from the grouted to hollow strength which diminished for higher block strengths. Shear walls with long effective flanges in relation to the web size also experience a higher discrepancy in P_r,max because the flange terms make up a higher portion of the total maximum load.

This bug ended up being very simple to find in the code and fix. It has been added to the known bugs page found here and will no longer be present in Versions 4.0 and newer.

Our Response

Bugs of this nature are taken very seriously. It was discovered in-house but not until very late in the Version 4.0 development process. As a result, the bug was investigated and a fix was added to Version 4.0. It has also been posted on our Known Bugs page where it links to this article.

If there is any question regarding the integrity of the results for a specific MASS project file, please feel free to contact CMDC directly. As the authorized MASS technical service provider, CMDC is available to help designers understand the specifics of identifying this issue, as well as any other masonry related technical questions. Click here for more information on technical assistance offered by CMDC.

As always, feel free to contact us if you have any questions at all. CMDC is the authorized service provider for the MASS software which is a joint effort of between CCMPA and CMDC.

Masonry Analysis Structural Systems is a versatile tool that can be used to accelerate many different aspects of masonry design. While most design scenarios easily fall within the scope of the software, there are occasionally cases where extra work must be done in order to get useful results from MASS. Pilasters are one such case where their behaviour is similar in many ways out-of-plane walls. In order for the wall module to be useful, the pilaster design must be adapted to fit within the constraints of the user interface.

The method in this post outlined below outlines how the pilaster length can be increased to the length used for wall designs in MASS. The remaining cross section properties can be input into MASS and then all of the loads applied must be proportionally adjusted to factor in the length increase. For example, if a pilaster must be lengthened by factor of 2.5 times its original length, the loads applied must also be increased by that same factor, effectively designing a larger section for a higher load in a way such that the results obtained using MASS are useful in determining the design of the pilaster assemblage. To jump ahead to the final summary at the end of this post, click here.

Disclaimer: By using MASS to assist in the design of a pilaster, it is up to you, the engineer, to ensure that all of the differences between pilaster behaviour and that of a regular masonry wall are properly accounted for within MASS. If there is any doubt of having a complete and comprehensive understanding of how to model these differences, it is best to perform these calculations by hand.

Additionally, while the MASS software is a trusted tool in the engineering community across Canada, all of the liability regarding the results and designs is placed on the end user. If there is any uncertainty as to whether the software is being properly applied, please consult MASS support, the included help documentation, or the end user license agreement. The contents of this article are offered as a resource to be used only if the user is aware that they are no longer working within the scope of the software and do so at their own risk. That being said, the Canada Masonry Design Centre is available to answer any questions about the content of this post.

Getting Started

In order to take into account the differences between a pilaster design and a regular out-of-plane wall design using MASS, there are multiple aspects that must be considered and accounted for regarding:

1. 1. How the section is modeled (click to jump to section modelling)
   2. How the loads are applied (click to jump to load application)

This post outlines a process which helps the engineer adapt the scope of the MASS software to the design of pilasters subjected to a combination of axial loads and one-way, out-of-plane bending.

Modeling a “Pilaster” unit using MASS

In order for MASS to be useful as a design tool when dealing with pilasters, it is important to first understand the similarities to an out-of-plane wall constructed using conventional stretcher masonry units. The relevant, shared aspects include face shells with a grouted center region with up to two layers of vertical reinforcement in the middle. While the software can easily design the wall shown on the left but not on the right (below), useful results can be obtained by identifying the common characteristics and applying them within the scope of the MASS wall module.

The biggest difference and reason why pilasters cannot be modeled within MASS is that the software performs wall designs exclusively on a per metre basis. While a pilaster is an isolated element within a wall system, it must be adapted to a one metre design length to fit within the wall module. Effectively, the software can only design modules that are exactly 1m in length so the only way to obtain equivalent results is to extrapolate the pilaster length and satisfy this constraint. Displayed below is a diagram of a pilaster superimposed over its corresponding modeled assemblage using MASS:

In order to create a wall design within MASS that will be useful in the design of a pilaster element:

1. The wall must be fully grouted.
2. The masonry unit geometry must be adjusted to match that of the pilaster unit.
3. The reinforcement placement and positioning must be specified to reflect where it would be placed within a pilaster unit

Understanding these three aspects will help ensure that a wall can be created that properly represents the pilaster used for the design.

Fully Grouting the Wall

Since the entirety of a pilaster cross section is grouted, its design in MASS must also be restricted to walls that are fully grouted. This can be changed using the drop down menu along the right side of the MASS input window, shown below:

If this is left using the default selection of partially grouted, any designs that do not place a bar in every cell will have a hollow component of all compression-related calculations.

Changing the Masonry Unit Dimensions

By making use of the Masonry Unit Database, it is possible to create a custom “pilaster” unit which can be used to take into account the different unit size and face shell thickness. The Masonry Unit Database can be found along the top toolbar between the “Bearing Design” button and the “Critical Load Envelope” drop down menu, shown below:

Using this database, a masonry unit with an increased nominal thickness and corresponding face shell thickness can be created and used for design. In this example, a 390mm thick pilaster unit is created (nominal thickness of 400mm)

Once the unit has been created, it will appear in the list of suppliers and unit lines under the “Masonry unit” heading in the MASS input window.

Placement and Positioning of Reinforcement

In order to design a wall of a finite length using a MASS wall module that designs walls on a per m basis, all of the properties need to be scaled proportionally to take the different section sizes into account. For example, if designing a 0.4m long pilaster with four 20M bars arranged in a box formation, there is a total of 600mm² of steel within each layer of reinforcement (1200mm² total between all four bars). If designing the equivalent 1m section using MASS, this is equivalent to 1500mm² of steel per layer (600mm² x 1.0 m/0.4 m) and a total of 3000mm² of vertical reinforcement in the entire metre long wall.

Evaluating Bar Sizes Placed by MASS

In the case of a 0.4m long pilaster being converted to a 1m long wall section, this is fairly intuitive for a wall design with bars placed at every cell (spaced at 200mm) since this length represents two cells of a regularly constructed wall. In a case like this where the ratio of pilaster bars to bars in the MASS design equals the ratio of pilaster length to MASS wall length (always 1m), the bar size placed by MASS will match the bars used in the final pilaster design. For example, a wall designed by MASS using two 20M bars placed in every cell will contain five bars per layer within the 1m design. This will correspond to the 0.4m long pilaster design with 2 20M bars placed per layer. When the pilaster length or number of bars per reinforcement layer is changed, the math does not work out as cleanly and an added step of looking at total areas of steel is introduced.

Changing where the steel is placed

By default for designs with one bar per cell, vertical bars are placed in the middle of the wall. As soon as 2 bars are placed in each cell, they are positioned such that the cover distance between the outer edge of the bar and the outside face of the wall equals the “side cover” value in the “Minimum Clearances” section of the input window. By default, the side cover value is 55mm but this can be increased to move the reinforcement further from the face of the wall. The “Bar separation” value (by default, equal to 25mm) is checked against after the steel is placed based on the specified side cover. If the bars are too close together, such that the distance between the inside faces of each bar is less than the specified bar separation, the design will be unsuccessful.

If the symmetric option is disabled above the vertical steel section of the input window, rather than place both bars according to side cover, the first bar is placed based on side cover with the second then positioned using the bar separation input field. MASS will then check to ensure that the specified side cover is also satisfies between the second bar and the other side of the wall. Note that MASS will automatically place the steel closer to the tension face of the wall where it is most beneficial as long as the wall is subjected to loading that results in single curvature deflection for all load cases.

Fully grouting the wall, making changes to the masonry unit, and adjusting the steel positioning is the closest a MASS wall design can come to resembling that of a pilaster.

Applying Loads to a Pilaster Modeled in MASS

Once the cross section of a pilaster has been modeled within MASS, loading is the only remaining consideration needed before the software can produce helpful design results. Without making any changes to the way loads would be applied to a conventional wall design, the results created by the software are completely invalid (and likely massively under designed for the loads it will be resisting)! Starting with a quick primer on how MASS loads out-of-plane walls, this article will outline how a load can be changed to factor in the changes made to accommodate pilaster design.

Refresher on MASS Wall Loads

It is a common misconception that lateral, distributed loads are applied to wall modules in the form of pressures, rather than line loads. This mistake is often made without consequence because MASS designs walls on a per m basis so when a pressure applied in kPa or kN/m² is divided by a one metre length, the result is a line load with the same magnitude as the initial pressure. For example, an unfactored wind pressure of 1.2kPa is applied in MASS as a line load of 1.2kN/m (per m of wall).

If the wall length were not exactly one metre, there would be a difference in magnitude between the applied wind pressure and the equivalent line load applied to the wall in MASS. For example, if looking at a 0.4m long pilaster, the same 1.2 kPa unfactored wind pressure would result in a line load of only 0.48 kN/m because the pilaster is resisting a much smaller tributary area of applied wind pressure.

If the pilaster were still resisting all of the wind load applied to a one metre length then this magnitude would be the same, just like in the regular wall example, shown above the pilaster example.

When determining the loading on a pilaster section, it is likely that there is a much larger tributary area of load transferred from the walls on either side. This often results in large lateral line loads that the pilaster must be designed to resist. Consider an example where pilasters are spaced 3.2m apart along a wall with lateral and axial loads transferred to the pilaster section through the walls spanning between them. With each pilaster having a tributary width of 3.2m, the equivalent line load for a 1.2kPa unfactored wind pressure would be 3.84 kN/m applied along the height of the pilaster.

Even after accounting for tributary area, there is further adjustment needed in order for MASS to be useful for pilaster design.

Converting your Pilaster Loads for MASS

Recall the pilaster section as it is represented in MASS described earlier in this article. The unit thickness, face shell thickness, grouted area, and reinforcement positioning have been adjusted in order to model the section using MASS with the only remaining difference being the cross section length:

The length of the “wall” being designed is unable to be changed from 1m so all applied loads must be scaled up to take the additional cross section into account. Since the design in MASS is wider than the actual pilaster by factor of MASS design length to pilaster length, the loads must also be scaled by the same factor. This can be done using the expression below:

By multiplying each applied load by the ratio of MASS wall design length to the actual pilaster length, the loads are adequately scaled to ensure that the factored loading and resistances are adjusted equally. Consider the example below with a lateral, uniformly distributed load of 3.84kN/m and an axial load of 40kN applied from the roof level:

Since the section designed in MASS is 2.5 times the length of the actual pilaster being designed (1.0m/0.4m factor), the loads applied to the assemblage in MASS must also be scaled up by that same factor. This relationship holds true for all load types beyond line loads and axial loads.

Self-weight

While it is in many cases conservative to let the software include self-weight automatically, it is recommended to manually calculate and apply the magnitude of the self-weight force resting upon the critical section of the pilaster. The option to include self-weight can be disabled by un-checking the box at the bottom of the loads application window, shown below:

When applying the self-weight manually, be sure to apply it as a dead, axial load at the top of the wall. Ensure that in addition to taking into account the total area of masonry supported above the critical section, also make sure to scale this load up using the formula discussed in the previous section. While the MASS calculated value will be correct based on the modeled 1m long section, it does not include any other masonry not modeled within MASS and also makes some conservative assumptions that might be the topic of a future article. The help files can always be consulted for an explanation on how self-weight is calculated.

Design Example

Looking at the elevation with 4m tall, 0.4m long pilasters spaced at 3.2m apart (referenced throughout this post), the results when calculated by hand can be compared to those of the MASS software to verify this approach. When the user has made the appropriate adjustments, the results produced by MASS can be valid for design purposes. The MASS file used to compare with hand calculations can be downloaded by clicking here. For simplicity, both the 40kN axial load and the 3.84kN/m line loads were applied as dead type loads so that there would be only one load combination, 1.4D. The exact pilaster unit created earlier was used for this exercise, having a 50mm thick face shell and the steel was placed such that layer 1 would be placed at d=290mm and layer 2 placed at d=100mm (achieved using a specified side over of 90.25mm). A summary can be seen below:

Note that nearly all of the values calculated by hand are directly proportional to their counterparts calculated using MASS. The only exceptions were measurements perpendicular to the length of the wall such as eccentricities, neutral axis locations, and deflections. While forces and moments all scaled proportionally, stress values such as v_m were the same between hand and software calculations because they are independent of length.

If there are questions about the processes or approaches used to get any of these numbers please do not hesitate to contact CMDC.

Limitations of using MASS to help with pilaster design

While the process outlined in this article can serve as a useful guide for assisting with the design of a wall containing pilasters, there are some limitations which must also be acknowledged and accepted.

Composite action with the walls on either side is not considered

In particular to cases where the flush side of the wall is also the compression face, the building can be designed such that there is composite action where the vertical reinforcement within the pilaster is coupling in tension with the compression side of the walls on either side.

There is no way to model this within MASS so any pilasters designed with the assistance of this guide will depend solely on the capacity of the pilaster element itself. If composite action is required, it is best to perform this design by hand.

Any vertical bars in compression are ignored

As specified by the CSA Standards, reinforcement in compression cannot be included when evaluating the capacity of any masonry element without being adequately tied. There is no way to tie the steel in compression within a masonry wall constructed using conventional stretcher units so it is absent from all wall designs performed by the MASS software.

Since there is no way to convey to the software that the reinforcement is tied within the wall module, there is no way to consider steel in compression.

No more than two layers of tensile reinforcement can be placed

MASS only has the ability to place up to two bars per cell and as a result there is no way to take additional layers of reinforcement within a pilaster into account. Even when there are only two layers of reinforcement in tension, there is no way to place varying areas of steel within each layer.

For example, if a pilaster were designed with reinforcement arranged in a three by three box formation, there is no way for MASS to place the area of three bars in the outermost layer and the area of two bars in the second layer. If a design requires more than two layers of tension reinforcement or a higher area of steel in the outermost layer, it is best to perform this design by hand.

…and one more thing to consider

As outlined in this post, there is considerable effort required to design a pilaster using MASS. While there are situations which warrant the use of pilasters, it may be worth considering the use of a conventional, rectangular wall constructed using a larger or stronger masonry unit. There is always the chance that it may be more economic to use a higher strength unit and resist the same loads without the need for pilaster units.

Summary

In general terms, this process can be summarized by saying that in order to model a pilaster using the wall module within MASS, the pilaster cross section can be scaled up to have a length of one metre. The loads must then be scaled upward by an equal amount to compensate for the increase in effective cross section. More specifically, the steps to accomplish this are outlines below:

The pilaster can be modeled with a longer cross section

Since the wall module in MASS only designs walls on a per metre basis, the pilaster must be modeled as having an increased length with all other properties specified accordingly.Click here to view more information on creating a pilaster section in MASS. 

Fully grout the wall

Specifying that the wall be fully grouted in MASS ensures that no hollow masonry properties are applied within the design. Placing bars spaced every cell with the partially grouted selection also accomplished this. Click here to jump back to the grout section.

Modify the masonry unit

Using the Masonry Unit Database, the geometry of the unit can be adjusted to increase the overall thickness of the masonry unit as well as the thickness of each face shell. A step by step guide on how to do this can be found by clicking here and expanding the database instructions.

Position the reinforcement

By default, MASS only places one bar in the middle of each cell. The selections can be expanded to place up to 2 bars per cell and where they are places within the unit can be adjusted by modifying the values in the minimum clearances section of the input window. Click here to jump to the steel positioning section.

All applied loads must be scaled proportionally to reflect the increase in length

Since the pilaster has been modeled as a larger section, all loads must be applied in such a way as to account for this change. Click here to read the full section on load application. 

Manually scale each load

Before any loads are applied within MASS, they must be scaled by the engineer to take the larger cross section into account. This is done by multiplying the magnitude of each load by the ratio of the length used by MASS to the length of the actual pilaster before applying them onto the wall in MASS. Click here for detailed instructions and an example to demonstrate how this can be done.

Manually calculate self-weight

While MASS can include self-weight automatically, there are limitations to how this is performed and which areas are taken into account. In particular to additional areas of masonry supported by the pilaster, it is best to manually calculate the self-weight before scaling the magnitude and applying to the wall within MASS. For more information, click here.

If you have any questions, please do not hesitate to call or email the Canada Masonry Design Centre.

The MASS software is a product of a joint partnership between CMDC and CCMPA. CMDC is the authorized provider for MASS Technical Support.

The Shearline module in MASS is a useful tool to quickly and easily determine how lateral, in-plane forces are distributed within a single elevation. While the scope of the shearline module is relatively basic and relies upon a number of simplifying assumptions in the analysis, it doesn’t take much time to gain an understanding of how these loads are distributed around openings and movement joints.

One of the required steps before the loads are distributed is for the user to review the position and geometry of each pier and decide whether it be modeled as “Fixed” or “Cantilever”. More specifically, as an elevation is laterally loaded, whether each element’s deflection would more closely resemble that of a fixed or cantilever shear wall. Below is an illustration of how a shear wall deflects when the top end fixity is left unrestrained, or cantilever (top), compared to a shear wall deflecting with the top end condition fixed, restricting only rotation (bottom).

While the difference has a big effect on the design of the shear wall (fixed top reduces factored moment by 50%, two critical sections instead of one), the important aspect when modelling a shearline is lateral stiffness and rigidity. Cantilever shear walls deflect more than those that are fixed from rotating therefore attracting less load relative to the other shear walls within the elevation. An example I posted online a few years ago is included below and runs through the entire process of designing a shear wall elevation using the Shearline module in MASS.

Looking at the example from the video, consider the two piers highlighted below:

The leftmost pier has nothing above it to restrict lateral rotation so it’s behaviour would more closely resemble that of a cantilever pier. Conversely, the pier on the right has a significant area of masonry which would more likely cause it’s deflected shape to more closely resemble that of a fixed pier.

How to decide of a pier is modeled as a Fixed or Cantilever shear wall

When MASS Version 2.0 was in development, CMDC looked into creating an algorithm that could look at an elevation and automatically designate each element as fixed or cantilever. Unfortunately, development of this functionality did not proceed very far because there was nothing in any building codes, CSA standards, or even consensus within the design community regarding what exactly constitutes fixity at the top of a shear wall. As a result, end fixities were left as direct user inputs, having to be manually assigned by the designer, using their professional engineering judgement, each time a Shearline is created.

Often when there is a difficult engineering judgement, the response it to make the more conservative decision. While there are other design decisions in the development of MASS where choices were made in the interest of remaining conservative, there is no clear-cut “conservative” decision when it comes to lateral load distribution. While a fixed shear wall deflects less (thus attracting a larger shear force due to the increased rigidity) compared to a cantilever shear wall, it is important to remember that lateral, in-plane load distribution is relative. What increases loading for one element will take away from all of the others.

It is no coincidence that the examples shown on the MASS website, in the help files (found by pressing F1 within MASS), in the CMDC Masonry Design Textbook, or shown here highlight cases that are not particularly controversial when it comes to differentiating between fixed and cantilever behaviour. As an example, consider Figure 40 (shown below) from section 6.2 of the MASS Help Files demonstrating a) highlighted piers that would behave as cantilever compared to b) highlighted piers that would behave as fixed shear walls:

The reality is that there are many cases in the middle that can be taken either way with arguments on both sides having valid and rational points. At the end of the day, it is left up to the judgement of the engineer to make the final call.

If you have any questions, please do not hesitate to call or email the Canada Masonry Design Centre.

The MASS software is a product of a joint partnership between CMDC and CCMPA. CMDC is the authorized provider for MASS Technical Support.

The MASS software is a useful tool for designing the individual structural elements of a masonry building. While there is a shearline module for simple, single-storey elevations, there is no such equivalent when it comes to multi-storey shear wall design (yet). It is left to the designer to model each element of their shear wall within MASS in a way that accurately represents its behaviour. This article will touch on a few of the major aspects that come up when using MASS for multi-storey designs.

To jump straight to a specific aspect, click the heading links below:

• Load Distribution
• Total Height
• Top End Fixity

Click here to jump straight to the summary. 

Load Distribution

Before diving into the multi-storey specifics of shear wall design, it is useful to first recall the scope of the shear wall module in MASS.

Shear wall module scope:

The shear wall module in MASS designs an individual shear wall element for in-plane moment and shear based on the loads that are applied to that individual element.

The shear wall module can be used for multi-storey buildings so long as the designer has taken into account the various ways in which a shear wall element interacts with the structure around it.

This includes:

• The accumulation of axial loads applied above the storey being designed
• The accumulation of lateral loads applied above the storey being designed
• Any overturning moments resulting from lateral loads applied above the top of the storey being designed

Example Exercise

Consider the example below, where the second storey of a four storey shear wall is being designed using MASS. In order to design the second floor shear wall element, all loads must be distributed to the top of the wall from all of the walls above. Each storey is 4m tall and all dead loads include self-weight.

Before expanding the solution, it may be a worthwhile exercise to calculate the solution yourself to test your skills.

Note: All axial loads are assumed to be placed at the centre of the wall and evenly resisted by the full cross section (no load dispersion is considered within the section). In cases where axial loads are applied with some eccentricity, this can be accounted for in MASS using an applied moment with a moment arm equal to the eccentricity of the load.

While distributing loads makes up the majority of the work needed to design multi-storey shear walls in MASS, there are still three other important aspects to consider.

Total Height

It is possible that while the full shear wall is not considered “squat”, an individual storey may have a height to length aspect ratio less than 1. In this case, it is important to change the total height to match the height of the full shear wall so that MASS doesn’t treat the individual storeys as squat shear walls. By default, the total height is set to the same value as the shear wall height so if it is unchanged, there may be an unnecessary reduction in moment resistance.

A full article explaining the difference between “Height” and Total Height” can be found here, including examples showing between 15% to 24% of moment resisting performance losses for not taking the total height into account.

End Fixity

When looking at a shear wall element within a larger shear wall, the objective is to take all aspects of being part of a larger shear wall into account. While there is an option in MASS to fix the top of a shear wall from rotating, the effect on the design can be seen in the difference in bending moment profile below:

Applying a rotational fixity at the top of the wall effectively divides the moment between the top and the bottom of the wall’s supports. While the “Fixed (R)” end condition was added to MASS for the purpose of shear wall designs with significant masonry above which prevent rotation, the scenarios where it is appropriately used would more closely resemble what is pictured below, taken from section 5-7 of the MASS Help files:

As a result, there is no need to change the end fixity of the top of the shear wall, as long as the loads have been properly distributed. Using the cantilever configuration for a multi-storey shear wall , it can be designed element-by-element, accurately designing each storey for the same shear and moment profile as would be used if the full multi-storey shear wall were designed at once.

Only by using the default cantilever fixity selection can an individual storey be adequately modeled without having to apply additional loads to cancel out the effect from a fixed top rotational end condition.

Summary

To quickly summarize, there are three main things to consider when designing a multi-storey shear wall using MASS:

1. Load Distribution: all loads not applied directly to the storey being considered must have their effects included. In particular, the accumulation of axial loads, lateral loads, and overturning moments due to loads applied from storeys above.
2. Total Height: To avoid being penalized for squat shear wall moment arm reductions, be sure to change the total height in order to accurately reflect the full height of the wall.
3. End Fixity: While it may at first seem reasonable to factor in the rotational stiffness from storeys above by changing the top fixity to Fixed (R), it will not result in a moment profile that accurately reflects the moments experienced by the storey in question. The default cantilever selection with properly distributed overturning moments is a more appropriate selection.

The MASS software is a product of a joint partnership between CMDC and CCMPA. CMDC is the authorized provider for MASS Technical Support.

If you have ever designed a multi-storey shear wall and wondered why the moment resistance is less than expected, the reason is likely CSA S304-14: 10.2.8:

MASS automatically identifies shear walls that have an aspect ratio less than 1 and designates them as squat shear walls. Keeping all calculations and design results in accordance with the CSA Standards, it also correctly reduces the moment arm of all steel in tension when applicable which is why there is a reduction in moment resistance. While it is often the first reaction of many users to assume that this behaviour comes from a bug in the software, MASS is behaving as intended.

Multi-Storey Applications

What if you are designing just one element within a larger shear wall where the element has an aspect ratio less than one but the full shear wall does not? Is it correct to be applying the reductions from clause 10.2.8 to elements such as these? Consider the example below:

This example which was used in the Multi-Storey Shear Wall Design article demonstrates an instance where this clause comes into play. The entire shear wall itself is clearly not squat as it’s aspect ratio is 3.2. As it is loaded, it is behaving as a non-squat shear wall so it is not correct to be applying clause 10.2.8 to the design of an individual storey. In order to design this wall in MASS, only the individual elements can be modeled and designed separately. As you can see, the wall input into MASS on its own is designated as a squat shear wall which is where the Total Height input comes in handy: it allows the user to tell MASS that while an element may be “squat”, it should not be treated as such.

“Height” vs. “Total Height”

The scenario described above is the reason multiple height inputs are available in MASS.

Height refers to the vertical dimension of only the shear wall element being modeled while Total Height refers to the vertical dimension of the full shear wall assemblage, beyond just what is being modeled.

If Storey 2 is modeled in MASS without any consideration of the larger shear wall it is apart of, it is designated as being squat as it’s 4/5 aspect ratio is less than one. When the total height is changed to the full 16m, the aspect ratio used to apply squat reductions from clause 10.2.8 increases to 3.2 and the result is an improved moment resistance.

Impact on Design

How much of a change does this make to a shear wall design? Using the example from earlier, when designing using a 20cm, 15MPa concrete masonry unit, taking the total height into account means the difference between using No. 15 and No. 20 bars placed exactly the same. If using No. 15 bars for both designs, the squat version of the MASS file would need to go all the way from a 15 to 30MPa strength unit to compensate. Furthermore, if the masonry and reinforcement properties were both fixed to the same design, the difference in capacity can be seen on the interaction diagrams below:

Comparison of moment envelope curves for shear wall design both including and neglecting the total height

For the critical load combination (#15: 0.9D + 1.4W), this means that the moment resistance of the wall is reduced from 1333.5kN*m to 1111.5kN*m, or by 222kN*m, simply by not taking the aspect ratio of the full wall into account!

This effect is further demonstrated in the example below where 70% of the vertical reinforcement is concentrated on either end of the wall. This significant reduction in moment is a direct result of a reduced moment arm for the steel that is in tension and furthest away from the compression zone. Note that this design uses the exact same materials simply arranged differently.

Comparison of moment envelope curves for shear wall design both including and neglecting the total height

There is now a 330 – 430kN*m reduction in the moment resistance compared to the 200 – 275kN*m reduction observed when the reinforcement is evenly distributed. One thing to note for all of these comparisons is that the difference in moment resistance diminishes when the applied axial load approaches P_f,max.

For those curious, a comparison of the uniformly distributed reinforcement and concentrated end steel designs can be found by expanding the section below:

If you have any questions, please do not hesitate to call or email the Canada Masonry Design Centre.

The MASS software is a product of a joint partnership between CMDC and CCMPA. CMDC is the authorized provider for MASS Technical Support.

When software bugs are found, notifications are posted in the MASS website Known Bugs page, on the MASS welcome screen, as well as here on the CMDC website software blog in an effort to be transparent and keep all MASS users informed. This issue was found within our own office as a result of an inquiry from a MASS user that resulted in this post. The bug was found some time after and as a result, the fix was incorporated into MASS Version 3.0, as well as a modified copy of Version 2.2 specifically to address this issue (click here to read more about Version 2.2.1).

This post outlines the conditions required to trigger this error, the designs where this could have affected design results, the details of the bug itself, and how to check to see if this bug is present in any MASS project.

Jump straight to:

• Bug Summary
• Background information
• What types of designs might be affected
• How to check if a design is affected
• Example
• Our Response

Bug Summary

Under a very specific combination of conditions, MASS may calculate the critical axial load for a reinforced wall, P_cr using both (EI)_eff of 0.4E_mI₀ and Φ_er of 0.75, resulting in a P_cr value that incorrectly combines aspects of reinforced and unreinforced analysis.

This bug only affects designs where all of the following conditions are met:

1. vertical reinforcement is not in tension
2. load combinations with steel in compression also govern the design
3. the wall experiences slenderness effects but is not a slender wall (kh/t > 30)

If MASS designs a wall where the vertical steel is in tension, all of the software’s results are correct. The same is true if any of the other conditions listed above is not true. The unlikely combination of circumstances is the reason why most wall designs are not affected and also why this bug has not been discovered until recently. This has been addressed in MASS Version 3.0 as well as in an updated Version 2.2.1.

Background information

If a wall is reinforced, why is it a problem to use the reinforced reduction factor when it comes to slenderness effects?

There is no problem as long as everything else in the calculations is also treating the wall as if it were reinforced. The issue comes from the way in which MASS sometimes treats the wall as if it were unreinforced when the steel is not in tension. This is done intentionally as ignoring the steel allows the software to use CSA S304 chapter 7 clauses governing the analysis of unreinforced walls when it is beneficial. This also assumes that the addition of steel to an unreinforced (but still grouted) wall will not reduce its capacity. For a full explanation on RM/URM analysis for reinforced walls, click here.

Differences between treating the wall as reinforced vs. unreinforced

Reinforced analysis compared to unreinforced differs in two ways when it comes to determining slenderness effects of a wall:

1. Φ_e vs. Φ_er – Resistance factors for member stiffness used for slenderness effects
2. (EI)_eff – Effective stiffness for consideration of slenderness

Resistance Factors – Φ_e vs. Φ_er

There are two different resistance factors that are used in calculating the critical axial compressive load used for determining slenderness effects; Φ_e for unreinforced walls, and Φ_er for reinforced walls. Click the heading below to expand the CSA references from which these resistance factors are based upon.

As stated at the beginning of this post, the bug is that for reinforced walls, the reinforced reduction factor is sometimes incorrectly applied, using Φ_er rather than Φ_e. On its own, this would not be an issue, however, when combined with the reinforcement assumptions used in determining effective stiffness, there can be a “mixing” of assumptions that results in this bug.

Effective stiffness – (EI)_eff

Similar to the resistance factors, the formula used to determine effective stiffness for slenderness effects is a function of whether or not the wall is reinforced. Effective stiffness, or (EI)_eff, for unreinforced walls is 0.4E_mI₀ while (EI)_eff for reinforced walls is 0.25E_mI₀ (where the applied eccentricity is relatively low, below the Kern eccentricity). Click the heading below to expand the CSA references related to effective stiffness.

Reinforced walls with low eccentricities have an effective stiffness capped at 0.25E_mI₀. Compared to 0.4E_mI₀ which is used for unreinforced walls, there is a 37.5% reduction in stiffness simply for using the reinforced equation for the same wall design. Taking advantage of the unreinforced effective stiffness is what also mandates the use of Φ_e rather than the higher Φ_er.

What types of wall designs are affected?

As mentioned in the summary shown here,

• vertical reinforcement is not in tension
  • c is greater than d for any bar
• load combinations where c exceeds d also govern the design
  • Load combinations with higher axial loads are more likely to have the neutral axis exceed d while load combinations with both low axial load applied with high bending moment are typically closer to a wall’s interaction diagram envelope curve
• the wall experiences slenderness effects but is not a slender wall
  • Slenderness ratio, kh/t, is greater than 10 – 3.5[e₁/e₂] specified in S304-14: 10.7.3.3.1 but less than 30 where axial load is governed by S304-14: 10.7.4.6.4

The only wall designs affected by this bug are those which have axial loads so high that the steel is no longer in tension AND experience slenderness effects without being classified as slender walls (S304-14: 10.7.4.6). Many wall designs that are governed by slenderness effects also require compression forces in masonry coupling with reinforcement in tension and are therefore not affected. For example, single spans with only self-weight and some nominal loads transferred from roof level are often not loaded with enough axial load to move the location of the neutral axis beyond the depth of steel in the wall.

Additionally, in order for a design to be impacted by the presence of this issue, the load combinations where the circumstances above are present must also be critical to the design. Load combinations with the highest axial loads (for example: 1.4D) are most likely to also be governed by load combinations using high lateral loads combined AND lower axial loads (for example: 0.9D + 1.4W).

It might even be easier to rule out the wall designs that are not affected:

• all slender walls are unaffected and correctly handled within MASS
  
• all walls using vertical reinforcement in tension (bars are ignored in compression as they cannot be adequately tied) are unaffected
• all walls that do not have any slenderness effects are not affected
  

Most wall designs fall into one (or more) of these three categories and it takes a special combination of circumstances to trigger a design that results in this bug affecting software result

How to tell if a design is affected

Check to see if the steel is in tension

Look at the location of the neutral axis and compare it to where the vertical bars are placed. If the distance to the neutral axis, c, is less than the depth to the layer of reinforcement, d, then the steel is in tension and your design is not affected.

In this example, a wall constructed using 15cm units (thickness of 140mm) can be checked to see if the steel is in tension by comparing the Neutral axis value in the Simplified Moment Results window to the steel depth, d, which is placed in the middle of the wall (b_w/2).

Steel is in tension (c<d)

Check to see if that load case governs the design result

As mentioned earlier, the load cases resulting in the steel not being in tension tend to differ from the load cases that govern the final design result (1.4D compared to 1.25D or 0.9D + 1.4W). When this is the case, the design is unaffected by the result. The example file highlights this aspect where the load combination resulting in steel being ignored (L.C. #1) is not critical to the design. In this case, load combinations 2 and 3 have total factored moments that are closer to the envelope curve which are based on the correct critical compressive axial load.

Out-of-plane wall designs tend to be governed by load combinations that combine the largest lateral load with the lowest axial load which are more likely to include steel in tension.

Note: To recreate this example for yourself, design a 3m tall, simply supported wall using 15cm, 15MPa units. Apply an unfactored axial dead load of 60kN, turn off self-weight, and apply an unfactored uniformly distributed wind load of 1 kN/m (or 1 kPa when considering a 1m length of wall as is the case for MASS wall modules). When designing for moment and deflection, at the first thing that will happen is that the wall will correctly pass being designed as unreinforced. For the purposes of highlighting this bug, de-select the 0 bars/cell option, effectively forcing reinforcement to be placed in the wall and skipping any iterations that are reinforced.

If the wall design is affected, compare the M_r to the manually adjusted value of M_f,tot

If the bug is present in a MASS project, the total factored moment resistance can be adjusted using the following expression:

M_ftotadjusted represents the adjusted value for the total factored moment taking slenderness effects into account

P_cradjusted represents the adjusted critical axial compressive load

P_crMASS is the critical axial compressive load calculated by MASS for load combinations where the bug is present in the results.

All other terms are defined within the CSA S304-14.

Both a derivation of the P_cradjusted expression as well as an example demonstrating how to use it can be expanded in the two sections below by clicking on each heading:

It is expected that most designs will not meet all of the criteria for the bug to be present as the reinforcement is in tension for most reinforced wall designs. For those designs where the bug is present, it is possible for the the marginal difference in total factored moment to result in a failed design which would have been thought to have passed moment and deflection design. As mentioned earlier, the specific and unlikely combination of circumstances required to trigger this bug within MASS is the likely reason why it has remained undiscovered for so long.

Our Response

Bugs of this nature are taken very seriously. It was discovered in-house but not until very late in the Version 3.0 development process after it had been initially thought to be complete. As a result, the bug was investigated and a fix was added to Version 3.0 as well as to Version 2.2 in the form of MASS Version 2.2.1 (included in the installation directory for Version 3.0 – click here to read more). It has also been posted on our Known Bugs page where it links to this article.

If there is any question regarding the integrity of the results for a specific MASS project file, please feel free to contact CMDC directly. As the authorized MASS technical service provider, CMDC is available to help designers understand the specifics of identifying this issue, as well as any other masonry related technical questions. Click here for more information on technical assistance offered by CMDC.

Length

A beam’s length represents the total length of the entire modeled assemblage including any overhanging length on the outside edges of the supports. This value is typically entered in first and must accommodate the length of the opening above which the beam is spanning as well as the bearing plates on either side. Any additional masonry outside of the primary span is not used when distributing loads and determining the factored moment or shear that must be resisted by the beam. Once specified for a new beam design, a clear span,explained below, is then assumed based on the length needed for bearing on either end.

Clear Span

The clear span refers to the length of the opening above which the beam is spanning. While a beam’s length is typically entered first into MASS, it is also possible to start a MASS design by specifying a clear span and let the software automatically fill in the total beam length based on the length required for bearing on either side, rounded to the nearest modular cell length.

Bearing Length

The bearing length is defined as the length along the beam under which a high concentration of stresses due to concentrated loads is transferred to the supporting structure below. It can be spread over a steel plate or an area of masonry under compression. The default bearing length of 300mm was chosen for MASS because it is the longest allowable bearing length (CSA S304-14: 7.14.1.2) that can use a triangular load distribution and not require additional detailing (ie. using a rocker plate) to ensure a rectangular load distribution. For triangular reaction distributions, the centre of reaction is at one third of the bearing length away from the edge of the clear span and for rectangular distributions, the distance to centre of reaction is at half of the bearing length.

Design Length

Design length is the distance between the centre of reactions between beam supports. It is less than the beam length and greater than the clear span, used to determine the factored moment and shear. For example, checking MASS results by hand and looking to replicate the maximum factored moment at mid-span for a simply supported beam, the design length is used in M_f = wL²/8.

Quick demonstration – From masonry elevation to design using MASS

Starting with an elevation containing an opening with masonry extending above and on either side, a portion must be designated as part of the modeled beam. This example where two courses are assumed for the beam’s height, the full beam length extends one full masonry unit to either side which allows room for the bearing area in addition to the clear span.

For the same elevation, it is also possible to design a single course beam or go all the way up to four courses which can all result in acceptable solutions. Smaller beams have reduced moment capacity mainly from a smaller moment arm between coupling tension and compression forces while taller beams can have intermediate steel requirements (S304-14: 11.2.6.3) and may also have to satisfy additional provisions for deep beams (S304-14: 11.2.7) and deep shear spans (S304-14: 11.3.6). Choosing how a beam is modeled is left to the discretion of the designer.

For all masonry beam designs, a load path for vertical loads must be assumed for transfer to the supporting structure below. The default bearing area with a bearing length of 300mm is shown below resulting in a triangular distribution of the reaction force. Had the bearing length been longer than 300mm, the reaction would have been spread over a rectangular distribution (S304-14: 7.14.1.2).

In order to determine the design length, the centre of each reaction force must be determined. For a triangular reaction distribution, this location is one third of the bearing length away from the edge of the clear span for each support. (Rectangular distributions have a centre of reaction point half way through the bearing area)

The locations of the reaction forces expressed as point loads is then used to determine the design span. They are also where MASS draws the support points underneath the bearing plates in beam drawings.

Note that the difference in unit arrangement between the figures above and MASS has no impact on the design as fully grouted masonry. MASS always starts an assemblage with a full unit however starting with a half unit as was done in the illustrations above is functionally the same design.

As always, feel free to contact us if you have any questions at all. CMDC is the authorized service provider for the MASS software which is a joint effort of between CCMPA and CMDC.

While there is no way around satisfying the minimum steel requirements in the CSA S304, there is a clause that can be taken advantage of that is not used by MASS. By following the procedure outlined in this article, beams can be designed within the restraints of the CSA standards while also containing less than the minimum reinforcement area as prescribed by clause 11.2.3.1. This often overlooked clause can be very helpful when it comes to masonry beam design, especially those that would seem at face value to be the easiest to design due to nominal loads and short spans.

July 2020 Update: This clause has been incorporated into the release of MASS Version 4.0.

Disclaimer: This post is exclusively intended to provide insight into the approach taken by the MASS design software in interpreting a CSA S304-14 code compliant design. It is up to the professional discretion of the designer to input an appropriate layout, boundary and loading conditions, interpret the results, and determine how they should be incorporated into their designs. As per the end user license agreement (and also recommended within PEO’s guidelines for using engineering software), a tool cannot be considered competent and reliance on a tool does not relieve the user of responsibility.

To jump straight to a summary further down the post, click here.

The smallest beams with only nominal loading can also be the trickiest to design. One of the reasons is the need to satisfy minimum reinforcement ratio requirements in S304-14: 11.2.3:

Currently in the MASS software, all beam designs not meeting ρ_min in clause 11.2.3.1 will fail moment and deflection design, shown below in the simplified moment results tab:

While these designs are failed before attempting an incrementally larger design with more reinforcement, there is an option at the engineer’s disposal outside of MASS: invoke the mighty power of clause 11.2.3.2 which often goes overlooked.

There was some initial due diligence behind including this clause in the MASS software. It was not included as programming costs would be very high. The change would involve functionally designing two beams; the first being the actual beam used for the design, and the second beam being the theoretical beam containing one third less reinforcement which would be used to resist the factored moment. While at first glance, it might seem acceptable to instead ensure that the beam has additional moment resistance by factor of 4/3. However, while it is very close, there is not quite a directly proportional relationship between a beam’s moment resistance and its longitudinal reinforcement area so this approach would not adequately reflect the phrasing of clause 11.2.3.2.

How to use this clause

There are two different approaches that can be taken to satisfy clause 11.2.3 and design a beam that contains less than the required reinforcement ratio, or ρ_min,  of clause 11.2.3.1:

Method 1

Compare the area of reinforcement to the area required by analysis increased by one third

Method 2

Compare the factored load to the load resisted by the beam if the reinforcement area were reduced by a third

Unfortunately, there is no way around completing a separate analysis to determine “the area of reinforcement required by analysis” quoted directly from the standard. Since the minimum reinforcement is a function of loading, one cannot be solved without assuming the other. Method 1 is likely more intuitive as it returns an alternative minimum reinforcement area to clause 11.2.3.1. However, Method 2 can be more straight forward to calculate as there is no need solve a quadratic or cubic function.

Method 1: Comparing areas of reinforcement

The approach taken in method 1 is to answer the question: “How much reinforcement is required in this beam design?”. This can be expanded to “What area of steel results in factored moment being equal to moment resistance?”. For beams with compression steel or intermediate steel which may not necessarily be yielding, it is likely easiest to solve for this value using a spreadsheet and GoalSeek or Solver since a simplified expression would likely require finding the roots of a cubic function and would also rely upon an assumed strain profile if the steel is yielding. Minimum reinforcement failure messages do not tend to present themselves for beams with several layers of steel so this article will focus on the simple beam designs where these issues arise.

The area of steel required, or A_sreq, can be solved for using force and moment equilibrium for any beam configuration where the beam’s moment resistance is equal to the maximum factored moment (M_r = M_f). The expression below can be used calculate this minimum area of reinforcement for beams with only tension reinforcement:

Note that this expression is only applicable to beams that exclusively contain primary tension steel to resist flexure (ie. no intermediate or compression steel). This formula also assumes that the tension steel is yielding which is a requirement in clause 11.2.2. Also, while the area of reinforcement required is typically a function of a beam’s moment resistance, it is possible that other factors such as cracking and deflection may govern the design and as such, should never be assumed to be satisfied and always checked manually (in addition to using this formula).

The units of each input are shown below as well as the derivation which can be expanded.

Method 2: Comparing Loads

Rather than ask the question, “What is the minimum area of reinforcement needed?” for a beam design, the other way to approach satisfying clause 11.2.3.2 is to assume that the area of steel present is equal to the minimum allowable and determine the largest possible factored moment that the assumption is valid for. Since this clause takes loading into account to evaluate minimum steel, rather than use a load to check the area of steel, method 2 involves using an area of steel to check the load. As mentioned earlier, this method may appear less intuitive as it is not as simple as comparing the reinforcement present to another minimum value. However, the steps used to determine the maximum allowable are the same as those used to calculate the moment resistance of any other beam design which is why method 2 may be preferable.

The table below shows a summary of the maximum allowable factored moments resisted by beams which contain less reinforcement than allowable by clause 11.2.3.1 for four possible beam geometries:

Maximum applied factored moment for a beams having less than the required reinforcement ratio in accordance with S304-14: 11.2.3.1 to satisfy S304-14: 11.2.3.2

Disclaimer: These values should not be relied upon as part of the design process. They are meant to illustrate the concept that very low areas of reinforcement may be acceptable, depending on the applied loads. The full cross section should be analyzed by the engineer by hand (or other tool) to check these requirements in a way that is applicable to the situation.

As stated under the simplified method 1 expression earlier, although the area of steel  required is typically governed by moment resistance, it is possible that other factors such as cracking and deflection may govern the design and as such, should never be assumed to be satisfied and always checked manually. 

Note that for designs using 2 No. 10 bars in tension (same bar area as 1 No. 15 bar), the placement is affected as the distance from the compression face of the beam is slightly further away from the vertical centroid of the bars. This change increases the moment arm separating the coupled internal forces and slightly increases the maximum allowable moment for these designs. The lower (and more conservative) values are shown in the table for simplicity however the comparison can be expanded below.

Final Summary

All hope is not lost when a beam design fails due to not satisfying minimum steel using MASS, which only checks against CSA S304-14: 11.2.3.1. It is possible to satisfy minimum reinforcement requirements by instead using clause 11.2.3.2 by approaching the design in one of two ways:

• Method 1: checking bar area against one third greater than the area resulting in M_f being equal to M_r
  • This can be done quickly for beams with only primary tension reinforcement using the following expression:

• Method 2: checking factored moment against moment resistance for a beam with a third less steel than what is actually present within the beam.
  • This can be quickly checked by comparing the factored moment to the maximum allowable moment in the table below:

Disclaimer: These values should not be relied upon as part of the design process. They are meant to illustrate the concept that very low areas of reinforcement may be acceptable, depending on the applied loads. The full cross section should be analyzed by the engineer by hand (or other tool) to check these requirements in a way that is applicable to the situation. Regardless of which method is used, it is up to the designer to ensure that in addition to satisfying the minimum reinforcement requirements in S304-14:11.3.2, all other provisions must be considered and independently verified. The guides in both methods are based on the area of reinforcement being governed by applied bending moment at any section within the beam which is not true for all cases.

As always, feel free to contact us if you have any questions at all. CMDC is the authorized service provider for the MASS software which is a joint effort of between CCMPA and CMDC.