Reduction factors in permissible stress of masonry

The permissible compressive stress in masonry cannot be taken equal to the strength of the unit or prism, because a real wall differs from the tested specimen. IS 1905 therefore starts from the basic compressive stress $f_b$ (Table 8; for a short, axially loaded member built of units of standard shape) and multiplies it by reduction factors:

$$f_c = f_b \times k_s \times k_a \times k_p$$

Role of each factor (IS 1905 cl. 5.4.1)

• Stress reduction factor $k_s$ (Table 9): accounts for the slenderness ratio and the eccentricity of the load. A tall, slender wall buckles at a lower stress, and an eccentric load causes bending. $k_s$ falls from 1.0 (SR $\le 6$) to as low as 0.15 (SR 27 with $e/t = 1/3$).
• Area reduction factor $k_a$: for small sections (area $A < 0.2$ m$^2$, such as columns and piers) the effect of local weak spots and poor workmanship is larger; $k_a = 0.7+1.5A$ ($A$ in m$^2$).
• Shape modification factor $k_p$ (Table 10): $f_b$ is based on the crushing strength of the unit, but for the same unit strength, masonry built with taller units has fewer bed joints and is stronger. Units with $h/w \le 0.75$ have $k_p = 1$; taller units get a factor above 1 (up to 1.8 for tall, low-strength units).

The factor of safety is already built into $f_b$. The reduction factors adjust it so that the allowed stress depends on how slender the member is, how it is loaded, how large its section is and what shape its units are. In design they are also used with the 25 percent increase allowed when $e/t > 1/24$ (cl. 5.4.1.4).