Question

4. The couple M acts in a vertical plane and is applied to a beam oriented as shown. Determine (a) the angle that the neutral axis forms with the horizontal, (b) the maximum tensile stress in the beam 45° 0.859 in M 25 kip in 4 in 4 in 6.74 in 1..= 21.4 in4

Answer 1

Iz=21.4 in⁴

Iy=6.74 in⁴

(a) Z_A=Z_B=0.859 in, Z_D=0.859-4 in=3.14 in

Y_A=-4 in, Y_B=4 in Y_D=-0.25 in

My=-25sin45= -17.67 kip-in

Mz=25cos45= 17.67 kip-in

Tan$\psi$=(IzTan$\theta$/Iy)

Tan$\psi$= 21.4Tan45/6.74

Tan$\psi$=3.17

$\psi$= -72.5

$\alpha$=72.5-45

$\alpha$=27.5 degrees

(b)

Maximum tensile stress occurs at D

$\sigma$_D= -M_zY_d/I_z+M_yZ_d/I_y

$\sigma$_D= -17.66x(-0.25)/21.4+(-17.66)(-3.141)/6.74

$\sigma$_D=8.42 ksi