Mechanics of Structure II Assignment: Buckling and Torsion Problems

This assignment solution addresses several key concepts in Mechanics of Structure II. It begins by analyzing the buckling behavior of a column under eccentric loading, determining the maximum load it can support. Following this, the solution delves into torsion problems, calculating shear stresses in circular shafts subjected to internal torques. Specific problems include determining shear stress at different points in a hollow shaft and analyzing the effects of applied torques on a solid shaft. Furthermore, the assignment examines the displacement of a gear tooth caused by torsional forces in a shaft. Finally, the solution concludes by calculating the angle of twist in a stepped shaft under applied torques. This assignment provides a comprehensive understanding of buckling, torsion, and shear stress calculations commonly encountered in mechanical engineering.

BET 201 Mechanics of Structure II
Class Activity - Week 10 –Buckling of Column (eccentric load)
and Torsion
Q1. The wood column is fixed at its base, and its top can be considered
pinned. Determine the maximum eccentric force P the column can
support without causing it to either buckle or yield. Take E = 10 GPa and
σ Y = 15 MPa
Figure 1

Q2. The hollow circular shaft is subjected to an internal torque of T =
10kNm. Determine the shear stress developed at points A and B.
Represent each state of stress on a volume element.

Q3. The pipe shown in figure 3has an inner diameter of 80 mm and an
outer diameter of 100 mm. If its end is tightened against the support at A
using a torque wrench at B, determine the shear stress developed in the
material at the inner and outer walls along the central portion of the pipe
when the 80-N forces are applied to the wrench.
Figure 3
Q4. The solid 30-mm-diameter shaft is used to transmit the torques
applied to the gears. Determine the absolute maximum shear stress on
the shaft.

Figure 4
Q5. The gears attached to the fixed-end steel shaft are subjected to the
torques shown in the figure. If the shear modulus of elasticity is 80 GPa
and the shaft has a diameter of 14 mm, determine the displacement of
the tooth P on gear A. The shaft turns freely within the bearing at B.

Figure 5
Q6. The 60-mm-diameter A-36 steel shaft (G = 75 GPa) is subjected to the
torques shown. Determine the angle of twist of end A with respect to C.

Figure 6