11.101 and 11.102 Each member of the truss shown is made of steel and has the cross-sectional area shown. Using E = 29 × 10 psi, determine the deflection indicated.
11.101 Vertical deflection of joint C.
11.102 Horizontal deflection of joint C.
Fig. P11.101 and P11.102
Calculate the vertical deflection of joint C
Answer to Problem 101P
The vertical deflection of joint C
Explanation of Solution
Given information:
The Young’s modulus of the steel (E) is
The area of the member BC
The area of the member BD
The area of the member CD
The vertical load act at the joint C (P) is
The horizontal load act at the joint C (G) is
The length of the member BD
The length of the member (L) is
Calculation:
Show the free body diagram of the truss members as in Figure 1.
Refer to Figure 1.
The length of the member BC
The length of the member CD
The length of the member BD
Show the free body diagram of the joint C as in Figure 2.
Here,
Refer to Figure 2.
Calculate the horizontal forces by applying the equation of equilibrium:
Sum of horizontal forces is equal to 0.
Calculate the vertical forces by applying the equation of equilibrium:
Sum of vertical forces is equal to 0.
Calculate the force act at the member CD
Substitute
Calculate the force act at the member BC
Substitute
Show the diagram of the joint D as in Figure 3.
Here,
Refer to Figure 3.
Calculate the vertical forces by applying the equation of equilibrium:
Sum of vertical forces is equal to 0.
Substitute
Partial differentiate the force act at the member BC
Calculate the deflection of the member BC
Substitute
Partial differentiate the force act at the member CD
Calculate the deflection of the member CD
Substitute
Partial differentiate the force act at the member BD
Calculate the strain energy of the member BD
Substitute
Calculate the vertical deflection of joint C
Substitute
Substitute
Hence the vertical deflection of joint C
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Chapter 11 Solutions
Mechanics of Materials, 7th Edition
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