N 1 The crosssection of a beam with a coordinate system that

N 1: The cross-section of a beam with a coordinate system that has an origin at the centroid C of the cross-section is shown. The normal strain at point A due to bending about the z-axis, and the Modulus of Elasticity are as given. Determine the internal bending moment Mz by the flexure formula 4 in e,r 200 ? rx 1 in E 8000 ksi 4 in in N 2: Draw the shear and moment diagram and determine the val-

Solution

let us determine the depth of centroid measured from the top of beam

let that depth be y

y=[(4*1*0.5)+(4*1*3)]/(4*1 + 4*1) = 1.75 in

moment of inertia of section about the centroid = 4*1³/12+(4*1*1.25²)+1*4³/12+(1*4*1.25²)=18.167 in⁴

let moment at section be M kip-ft = 12*M kip-in

stress at A= (12*M/18.167)*0.75=9*M/18.167

strain = 200*10^-6

modulus of elasticity=8000 ksi

9*M/18.167 = 8000*200*10^-6

M=3.23 kip-ft

Therefore, bending moment = 3.23 kip-ft