Masonry Magazine February 1994 Page. 4
MASONRY DESIGNERS' GUIDE
ALLOWABLE STRESS DESIGN
# GENERAL
Allowable Stress Design (ASD) is a method of proportioning structural members such that computed stresses produced in the members by nominal service loads do not exceed specified allowable stresses.
# NOMENCLATURE
* $A_n$ = Net cross-sectional area of member, in.² (mm²)
* $A_v$ = Net shear area of member, in.² (mm²)
* $b$ = Effective width of compression face of member, in. (mm)
* $b'$ = Width of concrete masonry bearing wall, in. (mm)
* $F_a$ = Allowable compressive stress due to axial load only, psi (MPa)
* $F_b$ = Allowable compressive stress due to flexure only, psi (MPa)
* $F_v$ = Allowable shear stress, psi (MPa)
* $f_a$ = Calculated compressive stress due to axial load only, psi (MPa)
* $f_b$ = Calculated compressive stress due to flexure only, psi (MPa)
* $f'_m$ = Specified compressive strength of masonry, psi (MPa)
* $f_v$ = Calculated shear stress, psi (MPa)
* $h$ = Effective height of member, in. (mm)
* $L$ = Span length of member, ft (m)
* $M$ = Maximum moment, in.-lb (N-mm)
* $P$ = Axial load, lb (N)
* $r$ = Radius of gyration, in. (mm)
* $V$ = Shear force, lb (N)
# AXIAL COMPRESSION AND FLEXURE
Members subjected to axial compression, or to combined axial compression and flexure, shall be designed in accordance with the following equations:
$f_a/F_a + f_b/F_b \le 1$
Axial compressive stress, $f_a$, shall be determined by dividing the axial load by the net cross-sectional area of the member. Flexural compressive stress, $f_b$, shall be determined by dividing the bending moment by the section modulus of the net cross-sectional area of the member.
The allowable compressive stresses due to axial load only, $F_a$, and flexure only, $F_b$, shall be determined as follows:
$F_a = 0.25f'_m [1 - (h/140r)^2]$ for $h/r \le 99$
$F_a = 0.25f'_m (70r/h)^2$ for $h/r > 99$
$F_b = 0.33f'_m$
# SHEAR
Shear stress, $f_v$, shall be determined by dividing the shear force by the net shear area of the member. The allowable shear stress, $F_v$, shall be determined as follows:
$F_v = 1.5\sqrt{f'_m}$, but not to exceed 75 psi (0.52 MPa)
For members resisting shear force by shear reinforcement, the allowable shear stress shall be determined as follows:
$F_v = 3.0\sqrt{f'_m}$, but not to exceed 150 psi (1.03 MPa)
# BEARING
Bearing stress on concrete masonry shall not exceed the following:
$0.25 f'_m$
This value applies only when the bearing area is not greater than one-third of the total area. When the bearing area is greater than one-third of the total area, the allowable bearing stress shall be permitted to be increased by multiplying by the following factor:
$\sqrt[3]{A_2/A_1}$
where:
$A_1$ = Bearing area
$A_2$ = Total area
STRENGTH DESIGN
# GENERAL
Strength Design is a method of proportioning structural members such that the computed forces produced in the members by factored loads do not exceed the design strength of the members.
# NOMENCLATURE
* $A_g$ = Gross cross-sectional area of member, in.² (mm²)
* $A_n$ = Net cross-sectional area of member, in.² (mm²)
* $A_s$ = Area of tension reinforcement, in.² (mm²)
* $b$ = Effective width of compression face of member, in. (mm)
* $d$ = Distance from extreme compression fiber to centroid of tension reinforcement, in. (mm)
* $E_m$ = Modulus of elasticity of masonry, psi (MPa)
* $E_s$ = Modulus of elasticity of steel, psi (MPa)
* $f'_m$ = Specified compressive strength of masonry, psi (MPa)
* $f_y$ = Specified yield strength of reinforcement, psi (MPa)
* $M_u$ = Factored moment, in.-lb (N-mm)
* $P_u$ = Factored axial load, lb (N)
* $\phi$ = Strength reduction factor
# AXIAL COMPRESSION AND FLEXURE
Members subjected to axial compression, or to combined axial compression and flexure, shall be designed in accordance with the following equations:
$\phi P_n \ge P_u$
$\phi M_n \ge M_u$
The nominal axial compressive strength, $P_n$, and nominal flexural strength, $M_n$, shall be determined in accordance with the provisions of TMS 402/ACI 530/ASCE 5.
The strength reduction factor, $\phi$, shall be as follows:
* Axial compression: 0.80
* Flexure: 0.90
* Shear: 0.80
# SHEAR
Members subjected to shear shall be designed in accordance with the following equation:
$\phi V_n \ge V_u$
The nominal shear strength, $V_n$, shall be determined in accordance with the provisions of TMS 402/ACI 530/ASCE 5.
# BEARING
Bearing stress on concrete masonry shall not exceed the following:
$0.60 f'_m$
This value applies only when the bearing area is not greater than one-third of the total area. When the bearing area is greater than one-third of the total area, the allowable bearing stress shall be permitted to be increased by multiplying by the following factor:
$\sqrt[3]{A_2/A_1}$
where:
$A_1$ = Bearing area
$A_2$ = Total area