1. A cantilever beam consists of a thin walled section of constant thickness (t). A vertically downward point load W is applied at the free end of the beam as shown in Fig. Q1. Using the values of W, L, B, D and t indicated in Table 1 and assuming Young's modulus E = 200kN/mm2 and shear modulus G = 77kN/mm2:
a. Find the principal second moments of area of the section.
b. Calculate the maximum direct stress due to bending and the orientation of the neutral axis.
c. Determine the maximum deflection of the beam due to bending only.
d. Find the maximum shear stress due to combined bending and uniform torsion.
e. If non-uniform torsion is taken into consideration, define the governing differential equation and boundary condition for the system under the applied torque. Hence, express the rotational displacement function and calculate the angle of twist at the free end. Find, also, the torque carried by St Venant torsion and warping torsion at the free end.
f. If the beam is subjected to an axial compressive force of 20kN through the centroid of the free end section besides the current applied load W, determine the magnitude and nature of the principal stresses at the centroid of the fixed end section.
g. If the tensile yield strength of the material making the beam σy = 300N/mm2, determine the factor of safety with respect to yield at the centroid of the fixed end section using Tresca and Von Mises theories.
Table 1. Values of the load and dimensions for Q1.
|
W
|
L
|
B
|
D
|
t
|
|
(kN)
|
(m)
|
(mm)
|
(mm)
|
(mm)
|
|
1.1
|
1.5
|
70
|
100
|
6
|
