The cross sectional dimensions of the beam shown in the figu

The cross sectional dimensions of the beam shown in the figure are a = 4.2 in. b axis is Mz 4.35 kip-ft. Determine (a) the maximum tension bending stress (a positive number) in the beam. (b) the maximum compression bending stress (a negative number) in the beam. 3 in d 4.2 in , and t 0 31 in The interna ending moment about the z centroidal typ) Answers: max T = .. .. psi psi

Solution

Let us determine the location of neutral axis and moment of inertia of section about the neutral axis

Let the depth of neutral axis measured from topmost face of beam be d

d = [(5.3*0.31*0.31/2)+(2*3.58*0.31*2.1)+(2*4.2*0.31*4.045)]/[(5.3*0.31)+(2*3.58*0.31)+(2*4.2*0.31)]=2.389 in

moment of inertia of section about neutral axis = 5.3*0.31³/12+(5.3*0.31*2.234²)+2*0.31*3.58³/12+(2*0.31*3.58*0.289²)+(2*4.2*0.31³/12)+(2*4.2*0.31*1.656²)=17.931 in⁴

Bending moment = 4.35 kip-ft = 4.35*12=52.2 kip-in

since bending moment is negative, tension is at top and compression is at bottom

maximum tension = 52.2*2.389/17.931=6.95 ksi

maximum compression = 52.2*(4.2-2.389)/17.931=5.27 ksi