Question one.
An assembly includes a steel rod CB and aluminum rod BA, each rod with a diameter of 12 millimeters. The rod is subjected to an axial loading A at the coupling B. Find the displacement of the B coupling and end A. upstretched length of each segment is shown in figure 1 below. The size of connections B and C is neglected and assumed that they are rigid.
Figure 1.
Solution
Given that Est = 200 GPa and Eal = 70 GPa.
Question two
An assembly has two steel rods and rigid bar BD. Each rod has a 20 millimeter diameter. A force of 50 kiloNewtons is applied on the bar as shown in figure 2 below. Find the vertical displacement of the load.
Figure 2
Solution
Given Est = 200 GPa
Here, referring to the FBD shown on the figure.
The cross-sectional area A of the rod is . Since the points A and C are fixed,
Here
Thus
Answer =
Question three
A concrete post is reinforced with 6 steel reinforcing rods each of 20 millimeter diameter. Find the stress of the concrete and steel when the post is subjected to axial loading of 900 kN
Figure 3
Solution
Given that Econ = 25 GPa and Est = 200 GPa.
Equilibrium;
.[1]
Compatibility:
. [2]
Solving equations [1] and [2] yields
Average normal stress:
Question four
A-36 steel rod with a 50 millimeter diameter is slightly attached to rigid supports at A and B at T1 = 80 °C. The temperature becomes T2 = 20 °C and the axial force of P = 200 kN is applied at the center. Find the reaction at A and B.
Figure 4
Solution
Referring to FBD of the rod
When the road is unconstrained at B, it has free contraction.
Using the method of super position
Substitute the result of into Eq (1),
Question five
Determine the maximum normal stress that is developed on the bar when subjected to a tension of P = 8 kN.
Figure 5
Solution
For and
