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 Shear Design

For right now I am going to cover basic shear design in accordance with MSJC 2005 / 2008 (AKA TMS 402/ACI 530). I will keep updating this for strength design and include some further discussion in the near future.

Ref 1. MSJC 2008 (2005 is very similiar however these provisions change for 2011) Building Code Requirements and Specification for Masonry Structures and Related Commentaries (AKA TMS 402 or ACI 530). Found here

Design and Analysis of Masonry Subject to Shear Forces

This will be a more indepth look at shear forces and how they are handled in masonry design and analysis.

There are several design methods / configurations to consider.

1. Unreinforced Masonry – ASD (Allowable Stress Design)
   • All members (flexural and shear walls)
2. Reinforced Masonry – ASD
   • Flexural members
   • Shear walls
3. Unreinforced Masonry – STR (Strength Design)
   • All members (flexural and shear walls)
4. Reinforced Masonry – STR
   • Flexural members
   • Shear walls

ASD Methods:

MSJC-08 provides a flowchart for shear design in the commentary (Figure CC-2.3-2) which is very helpful. Also allowable stress may be multiplied by 4/3 for short term loads – wind and earthquake per ASCE7-05 C2.4.1. However make sure that you are only multiplying the end result and not f’m found in the equations and the end result.

Here are the basics – Is the section subjected to a net flexural tension stress (i.e. P/A-M/S, is the stress negative)? If no then calculate the shear stress using fv = VQ/In*b where V=shear force, Q=first moment of area, In= net section moment of inertia and b=width or thickness of section. Then base the allowable stress on an unreinforced masonry section (not to be confused with a reinforced section w/out reinforcement). If there is net tension and the wall is reinforced (with longitudinal reinforcement for bending stress)  then find the shear stress using fv=V/(b*d). Base the allowable stress a reinforced wall section (flexural member or shear wall as applicable).

Unreinforced Masonry ASD (MSJC Section 2.25)

 In-plane Shear Forces (shear walls):

Allowable shear stress without any reinforcement (Ref 1 Section 2.2.5.2):

• Fv = Minimum of
  • 1.5x
  • 120 psi
  • 37 psi + 0.45 (For running bond masonry not grouted solid)
  • 37 psi + 0.45 (For stack bond masonry with open end units and grouted solid)
  • 60 psi + 0.45 (For running bond masonry grouted solid)
  • 15 psi

Out-of-plane Shear Forces (Ref 1 Commentary 2.2.5):

In MSJC 2005 and 2008 the commentary suggested that section 2.2.5.2 be used due to the absence of suitable research data.  This is shown above for In-Plane shear forces. However, in 2011 the MSJC, the code states (section 8.2.6.3) that the minimum normalized web area shall be 27 in^2/ft which provides sufficient web area so that hte shear stresses between the web and face shell of a unit will not be critical for out of plane loading.

Allowable shear stress without any reinforcement (Ref 1 Section 2.3.5.2.2):

• Fv = See above (same as in plane)

Reinforced Masonry ASD (MSJC Section 2.3.5):

Flexural members:

Allowable shear stress without shear reinforcement (Ref 1 Section 2.3.5.2.2):

• Fv= minimum of:
  • sqrt(f’m)
  • 50 psi

Allowable shear stress with shear reinforcement (Ref 1 Section 2.3.5.2.3):

• Fv= minimum of:
  • 3*sqrt(f’m)
  • 150 psi

Shear Wall:

Allowable shear stress is based on the ratio of M/(V*d) where M=moment V=shear force and d=depth from extreme compression fiber to tension reinforcement

Allowable shear stress without shear reinforcement (Ref 1 Section 2.3.5.2.2):

• Fv for M/(V*d) < 1 = minimum of:
  • 1/3*(4-(M/(V*d))*sqrt(f’m)
  • 80-45*(M/Vd)
• Fv for M/(V*d) >= 1 = minimum of:
  • sqrt(f’m)
  • 35 psi

Allowable shear stress with shear reinforcement (Ref 1 Section 2.3.5.2.3):

• Fv for M/(V*d) < 1 = minimum of:
  • 1/2*(4-(M/(V*d))*sqrt(f’m)
  • 120-45*(M/Vd)
• Fv for M/(V*d) >= 1 = minimum of:
  • 1.5*sqrt(f’m)
  • 75 psi

Shear Reinforcement Required (MSJC 2.3.5.3):

Shear reinforcement is designed for the entire shear force.

• Area of reinforcement parallel to shear force
  • Avpar=V*S/(Fs*d)
  • V=Shear force, S=vertical spacing of horizontal reinforcement  Fs = Allowable steel stress (with 1/3 increase as applicable) and d=distance from extreme compression to tension reinforcement
  • Max spacing is the lesser of d/2 or 48″
• Area of  reinforcement perpendicular to shear force:
  • Avv = 1/3 * Avh
  • Max spacing is 8′ o.c.

Strength Design Methods:

Will update soon.

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