Masonry Subject to Compression and Flexure – Stability – ASD

References

Ref 1 ACI 530/ASCE 5/TMS 402 direct number references are for the 2005 version however the method does not change up to the 2013 version. Found here

Ref 2 Masrony Structures Behavior and Design by Robert G. Drysdale, Hamid, and Baker 2nd Edition. (the Third edition found here)

Ref 3 Reinforced Masonry Engineering Handbook 6th Edition by Max Porter. Found here

Overview / Discussion

This pertains to stability of reinforced masonry subject to compression and flexure. Now when I first started to post about this subject I was a bit confused as I started digging into the code. Here’s what I mean. In my experience it seems that most engineers Most of us are used to some sort of moment magnifier when axial and moment forces are present such as in ACI 318 and AISC’s Steel Construction Manual. However, when we are designing masonry with ASD provisions we do not seem to find this when we read through the reinforced masonry section of ACI 530 (section 2.3.2 in the ’05 code). We don’t seem to find any adjustment or magnifier for second order / slenderness effects. This had confused me for sometime. I was setting up calculations using force equilibrium and compatibility equations similar to reinforced concrete (Only instead of an approximate rectangular stress block a triangular shape is used assuming a linear elastic stress distribution). Then in the analysis of the section you can directly solve for or iterate to find the location of the neutral axis. Well in doing this you are checking that the masonry is not crushing and also checking that there is adequate tension strength in the steel reinforcement, both of these are what I would say are ‘material’ checks. Meaning that you are checking the capacity of the local material not the overall member which may have less of a capacity due to buckling (stability check). You may say that there is a check for buckling, and that would be true. The required axial force vs the allowed axial force (eqn 2-17 and 2-18 in Ref 1). This however does not account for any moment which may be present. This to me did not seem right as there was no interaction in these equations for axial, moment and buckling. So I dug a little deeper and here is what I found.

Some Quick Background To Clarify My Point

I just want to provide some comparison and clarity for what I am referring to when I’m talking about second order / slenderness / stability effects. These effects are the results of the axial force and the deflection of the member which create ‘secondary’ moments. We can account for these effects in a number of approximate ways. If we go back to Timoshenko’s Theory of Elastic Stability we see that we can account (approximately) this additional bending moment by multiplying the first order moment, M by where is the required axial force as found from the results of a first order analysis and is the critical buckling load. We find this amplification in a number of design manuals – AISC 9th edition for a member subject to combined forces. However this formula was removed from the ‘design side’ of the AISC equations and is now found in the ‘analysis side’ in the form of B1 (see chapter c of the AISC 13th edition). This is also found in ACI 318 in the moment magnification procedure. We even find it in the strength design section of the ACI 530 (ref 1). However the procedure if for slender walls and differs from the ACI and AISC approach. In ACI 530 the deflection due to the applied loads is found, then the moment due to axial is found which causes additional deflection. The process is repeated with the new moments until successive trial results in less than 2% error (convergence).
Knowing this now and then reading through Ref 1 ASD design for reinforced masonry we start to think ‘hey something seems to be missing’. Well it is, sorta. Lets take a look.

Design – ASD

UPDATE – this was my first attempt to reason that there was some sort of provision in the code that was considering stability, but ultimately I was wrong. I am leaving this in, for reference.

Whether you are designing reinforced masonry or unreinforced masonry you basically are going back to the unreinforced masonry equations anyway so lets look at reinforced masonry.

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1. Reinforced Masonry
   1. Members must satisfy a buckling check given by eqn 2-17 or 2-18 in Ref 1, depending on the h/r ratio.
      1. This is basically a pure axial buckling check, no secondary moments
   2. “The compressive stress in the masonry due to flexure or due to flexure in combination with axial load shall not exceed f’m/3 ”
      1. This is what I was referring to as more of a ‘local’ material failure check as stability does not come into play with these equations.
   3. “The axial load component fa does NOT exceed the allowable stress Fa given in section 2.2.3.1” of Ref 1 which is the unreinforced masonry allowable compressive stress section
      1. Notice that you are only checking the axial stress component not the combined stress.
      2. This is ultimately where stability is check but it is not obvious at first. So we look further.
2. Unreinforced Masonry (section 2.2.3 in Ref 1)
   1. fa/Fa + fb/Fb < 1
      1. Unity check
   2. P<1/4 Pe
      1. Where Pe is simply a buckling equation limit to safegaurd against a premature stability failure caused by eccentricity of an applied axial load. Therefore in equation 2-15 (Ref 1) e is the actual eccentricity of the applied load (min value typically = 0.1t) not M/P where M is caused by other than eccentric load.
      2. Does this e consider deflection?

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I ended up contacting MSJC and received an excellent response from a Mr. Art Schultz from the University of Minnesota. I would like to add that I am very appreciative of Mr. Schultz and MSJC’s assistance. Also the “masonry community” in general seems to be very helpful.

Here the response:MSJC Stability Treatment ASD Axial and Flexure

To summarize: The code does not address stability / second order effects for reinforced masonry design using ASD.

I would say use the LRFD approach, it’s not so bad, see here.

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Masonry Columns, Piers and Pilasters

How to analyze and design reinforced masonry columns, piers and pilasters and clarifying effective spacing.

For analysis of masonry members utilizing flanges and compression reinforcement see Masonry – Compression Reinforcement and Effective Flanges

References

Ref 1: MSJC – 2005, TMS 402 (AKA ACI 530) – 05 (2008 version is very similar). Found here

Ref 2: Masonry Structures Behavior and Design 2nd Edition by Robert Drysdale, Hamid, and Baker.  (the Third edition found here)

Ref 3: Reinforced Masonry Engineering Handbook Clay and Concrete Masonry 6th Edition, Max L Porter (James E. Amrhein original author). Found here

Definitions

Based on MSJC 05 (all should be similar for 08)

Column

(MSJC-05 Section 1.6) – An isolated vertical member whose horizontal dimension measured at right angles to its thickness does not exceed 3 times its thickness and whose height is greater than 4 times its thickness.

Pier

(MSJC-05 Section 1.6) – An isolated vertical member whose horizontal dimension measured at right angles to its thickness is not less than 3 times its thickness nor greater than 6 times its thickness and whose height is less than 5 times its length. In reference to MSJC these are typically part of wall frames (see Ref 3 page 250) and is why there dimensions are defined as such. This however may be confusing as many times a pier is referred to a column which is built integrally with a wall (see pg 403 of Ref 2). Having said that I believe if the column is built integrally with the wall it would be considered a “flush pilaster” (see Ref 3).

Pilaster

–  While Ref 1 does not give an explicit definition of a pilaster, it does infer that a pilaster is built integrally with the wall. Ref 2 states that a pilaster is a column that is built integrally with a wall and interacts with the wall to resist an out-of-plane lateral load, it is called a pilaster. Pilasters maybe ‘flush’ (in the plane of the wall) or project out from the wall in one or both directions.

Pedestal

– Upright compression member with a ratio of unsupported height to average least lateral dimension not exceeding 3. This term is typically found in concrete design and

refers to short foundation elements. Many may refer to pedestals as piers or foundation piers.

Foundation Piers

– (Ref 1) An isolated vertical foundation member whose horizontal dimension measured at right angles to its thickness does not exceed 3 times its thickness and whose height is equal to or less than 4 times its thickness.

Wall

– (Ref 1) A vertical element with a horizontal length to thickness ratio greater than 3, used to enclose space.

Loadbearing Wall

– (Ref 1) a Wall carrying vertical loads greater than 200 plf in addition to its own weight.

Discussion

As you can see these elements may be referred to one another as they all are used to resist axial and flexure. I would need to check the 2011 version of the MSJC but it should also be noted that Piers are found in the Strength Design of Masonry only and Pilaster are only found in the ASD method. However lets look at how the analysis and design differs for each. I think some main points to consider are – Is the element isolated or part of wall construction? If the element is isolated it would generally be considered a column or pier. If it is part of a wall system then it would generally be considered a pilaster or flush pilaster. The main difference then between these is that for column/pier elements there is – added vulnerability due to isolation, typically compression reinforcement and potential for bi-axial bending. Another key to remember is that if the reinforcement is going to be considered to be effective in compression, the enforcement must be tied (confined) for any of the above mentioned elements.

Now lets look at how each classification effects the design.

Design

Dimensional Constraints / Effective Widths

This can be hard to keep track of as well. How much of the wall should be taken as effective to resist axial and flexural loads? What are the limits on effective flange widths? It is interesting to note that Ref 3 pg 177 limits the effective flange for pilasters to 3x the wall thickness each side of the pilaster however allows for 6x wall thickness for effective flange width on flanged masonry shear walls.

Effective Width

1. Walls – (ref 1 Sect. 2.3.3.3)
   1. Out-of-plane Forces – Running Bond Effective width shall be the lesser of:
      1. Center – Center spacing of bars
      2. 6 x wall thickness
      3. 72 inches
      4. H/6 in the case of a flanged shear wall. Where H is the total wall height (between lateral supports transferring load to the load to the shear wall).
   2. Axial Concentrated Load – Effective width
      1. 4 x wall thickness + bearing width or length of wall
   3. Design for Axial and Flexure
      1. The reinforcement is rarely tied and typically only resists tension forces.
      2. For ASD if the load is concentrated then the 4x the wall thickness limit would apply otherwise the limits presented in point 1 would apply and the reinforcement would need to be tied if it going to be relied upon to carry compression forces.
   4. In-Plane Forces – Flanged Shear Walls
      1. ASD – The flange is limited to 6x wall thickness each side of the web (Ref 3 pg 199)
      2. Wall intersections shall meet Ref 1 – Section 1.9.4.1
2. Flush Pilasters  
   1. Effective Wdith
      1. Tpcially taken as 4 x wall thickness (Ref 3 page 178)
3. Pilasters
   1. Effective width
      1. Ref 1 and 2 – 6 x Wall thickness each side of web
      2. Ref 3 – 3 x Wall thickness each side of web
   2. Consideration for flanges to be effective (see Ref 1 – 1.9.4.2).
      1. Flanges  (wall intersections) must be capable to transfer the required shear stress
      2. Atleast 50% of the masonry units at the interface shall interlock; or Steel connectors grouted into the wall (1/4″x1.5″ x28″ inculding 2″ long 90 deg bend at each end to form a U or Z shape; or Intersecting bond beams shall be provided in intersecting walls at a maximum spacing of 48″ oc (As = 0.1 in^2 and shall be developed on each side of intersection)
4. Piers
   1. Limits on Width
      1. The width should be greater than 3 x thickness but less than 6 times its thickness
         1. I believe if it were less than 3 x thickness it would then be a column and if it were greater than 6 it would then be a wall.
   2. Design limitations – Strength Design
      1. Max factored axial load (per Ref 1 3.3.4.3.1)
      2. Max effective height should not exceed 25 x nominal thickness unless the pier is designed according to provisions of Ref 1 Section 3.3.5 (walls, must consider P-Delta effects)
      3. Nominal thickness should not exceed 16″
      4. Provide (1) bar in the end cells and minimum area of longitudinal reinforcement should be 0.0007bd
      5. Uniformly distribute reinforcement
5. Column
   1. Limit on Width (Ref 1 – 2.1.6)
      1. Horizontal dimension measured at right angles to its thickness does not exceed 3 times its thickness. Minimum side dimension should be 8″
   2. Limits on Height
      1. Height is greater than 4 times its thickness
      2. Ratio of Effective Height / least nominal dimension < 25 (Ref 1 – 2.1.6.2)
   3. ASD Requirements (Ref 1 Section 2.1.6
      1. Min Side Dimension – 8″
      2. Height / least nominal dimension <= 25
      3. Min Moment should be 0.1 x each side dimension
      4. Min longitudinal reinforcement and shall at least 4 bars
      5. Max long reinf
      6. Compression reinforcement shall met lateral tie requirements (as always)
   4. SD (strength design) Requirements (Ref 1 Section 3.3.4.4)
      1. Same as ASD except that the provisions limit the distance between lateral support should be limited to 30 x the nominal width where as ASD uses ‘effective height’ (meaning considering end restraints) should be < 24 x thickness. Also max reinforcement shall be per Ref 1 Section 3.3.5 but not to exceed  
6. Lateral Ties
   1. Requirements (Ref 1 Section 2.1.6.5) If reinforcement is to be considered effective in resisting compressive forces lateral ties must be provided.
      1. 1/4″ diameter (min)
      2. Vertical spacing < smaller of –
         1. 16″
         2. 48 lateral tie bar diameters
         3. least cross-sectional dimension
      3. Every corner and alternate longitudinal bar shall have lateral support provided by the corner of a lateral tie (angle should be less than 135 deg). Except for a circle arrangement which is permitted. No bar bar shall be farther than 6″ (each side) from a laterally supported bar. (i.e. the middle bar should be less than 6″ from 2 bars that are laterally supported by a lateral tie ‘corner’)
      4. Place lateral ties in mortar joint or grout
      5. Lap length shall be 48 tie diameters (min)
      6. Locate the first and last lateral tie at 1/2 spacing.  Also above and below single beams framing into the vertical member.
      7. Where beams or brackets frame into a column from four directions ties may be terminated 3″ (max) from the lowest reinforcement in the shallowest of the beam members framing into the column.

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