Question

Answers:

M_max = 170.67×10⁶ Nmm

σ_{b max} = 248.42 N/mm²

F.O.S. = 1.24

5. Calculate the maximum moment in the beam shown. If the elastic section modulus of the beam is Z 687000 mm3, calculate the maximum bending stress in the beam. Calculate the factor of safety against failure if the design stress of the steel is ơd 309 N/mm2. 12 kN/m 8m 4m Fig. Q5

Answer 1

Take sigma M_A = 0 we get R_B times 12 - 12 times 8 times 8/2 = 0 implies R_B = 32 KN Also R_A + R_B = (12 times 8) implies R_A = 64 KN Now M_x = 64 x - 12 times x times x/2 = 64 x - 6x^2 For max B m partial_mx/partial x = 0 implies 64 - 12 x = 0 or x = 5.334 m therefore M_max = 64 times 5.334 - 6 times 5.334^2 or M_max = 170.67 or M-max = 170.67 times 10^6 N - mm Now we know sigma = M_max/z or sigma = 170.67 times 10^6/687000 implies sigma = 248.42 N/mm^2 Also FoS = sigma_d/sigma or Fos = 309/248.42 or FoS = 1.24