The cantilever beam is subjected to a concentrated load P Th

The cantilever beam is subjected to a concentrated load P. The cross-sectional dimensions of the rectangular tube shape are shown in the second figure. Assume b=108 mm, d= 255 mm, y_H = 108 mm, y_H = 60 mm and t = 8 mm. Compute the value of Q that is associated with point H, which is located 108 mm above the centroid of the rectangular tube shape. If the allowable shear stress for the rectangular tube shape is 164 MPa, determine the maximum concentrated load P that can be applied to the cantilever beam. Answers: Q =____________mm^3. P =____________kN.

Solution

Calculate the moment of Inertia Iz

Iz = Io - Ii

Iz = [(b*d^3)/12] - [(b - 2t)*(d - 2t) /12]

Iz = [108*(255^3)/12] - [(108 - 2(8))*(255 - 2(8))^3 / 12]

Iz = 44567662.7 mm^4

a)

Calculate Qmax

Qmax = [b*t*(d - t) / 2] + [2t * ((d/2) - t)] * [((d/2) - t) / 2]

Qmax = [(108)(8)((255 - 8) / 2)] + [2(8)((255/2) - 8)] * [( (255*2) - 8) / 2]

Qmax = 220946 mm^3

b) If the maximu shear stress is tmax = 164 MPa, the concentrated load P is

tmax = (P*Qmax) / (Iz*t)

P = (tmax * Iz * t) / Qmax

P = [(164 x 10^3) (44567662.7) (2*8)] / 220946

P = 529294700.6 kN = 5.29 x 10^8 kN