# 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.

- Unreinforced Masonry – ASD (Allowable Stress Design)
- All members (flexural and shear walls)

- Reinforced Masonry – ASD
- Flexural members
- Shear walls

- Unreinforced Masonry – STR (Strength Design)
- All members (flexural and shear walls)

- 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.

Looking forward to the Strength design update.