The assembly consists of two A992 steel bolts AB and EF and an 6061-T6 aluminum rod CD. When the temperature is at 30° C, the gap between the rod and rigid member AE is 0.1 mm Determine the normal stress developed in the bolts and the rod if the temperature rises to 130° C.
Assume BF is also rigid.
R4–1/2
The normal stress developed in the bolts and rod.
Answer to Problem 4.1RP
The normal stress developed in the bolts and rod are
Explanation of Solution
Given information:
The two bolts AB and EF are made of A992 steel.
The rod CD is made of 6061-T6 aluminum.
The Young’s modulus of the steel is
The Young’s modulus of the aluminum
The coefficient of thermal expansion of the steel
The coefficient of thermal expansion of the aluminum
The initial temperature
The finial temperature
The gap between the rod and rigid member AE is
The diameter of the bolts AB and EF
The diameter of the rod CD
The length of the bolts AB and EF
The length of the rod CD
Calculation:
Calculate the area of the bolts AB and EF
Substitute
Calculate the area of the rod CD
Substitute
Calculate the difference of temperature
Substitute
Show the free body diagram of the rigid cap as in Figure 1.
Refer Figure 1.
Calculate the vertical forces by applying the equation of equilibrium:
Sum of vertical forces is equal to 0.
Here,
Show the initial and final position of the assembly as in Figure 2.
Refer Figure 2.
Here
The deformation is as follows:
Substitute
Calculate the force at the bolts AB and EF
Substitute
Calculate the force at the rod CD
Substitute
Calculate the normal stress developed in the bolts AB and EF
Substitute
Calculate the normal stress developed in the rod CD
Substitute
Hence, the normal stress developed in the bolts and rod are
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