A cross section of a beam is subjected to internal loadings

A cross section of a beam is subjected to internal loadings, M_z = 26KP ? and V_y =1200 , as shown below. Determine (a) the bending (normal) stress at A due to the bending moment (M), (b) the shear stress at A due to the shear force (V). (c) Draw a 2-D stress element showing the state of stress at A using stresses from (a) and (b). (d) Draw a Mohr’s circle and (e) determine principal stresses, principal plane, and the maximum shear stress from the Mohr’s circle.

Solution

Location of the neutral axis:

a) , where is the distance from A to the neutral axis. Let’s compute the moment of inertia.

Finally

b) , where and

So

c) 2D- Stress state

d) Center: .

Radius:

e) Principal Stresses:

Maximum shear stress: