11.103 and 11 104 Each member of the truss shown is made of steel and has a cross-sectional area of 500 mm2. Using E = 200 GPa, determine the deflection indicated.
11.103 Vertical deflection of joint B.
11.104 Horizontal deflection of joint B.
Fig. P11.103 and P11.104
Calculate the horizontal deflection of joint B
Answer to Problem 104P
The horizontal deflection of joint B
Explanation of Solution
Given information:
The Young’s modulus of the steel (E) is
The area of the each member (A) is
The vertical load act at the joint C (P) is
The length of the member AD
The length of the member CD
Calculation:
Consider the horizontal force (Q) at joint B.
Show the free body diagram of the truss members as in Figure 1.
Refer to Figure 1.
Calculate the length of the member AB
The length of the member BD
The length of the member AD
The length of the member CD
Calculate the length of the member BC
Show the 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
Show the diagram of the joint B as in Figure 3.
Here,
Refer to Figure 3.
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 BD
Substitute
Calculate the force act at the member AB
Substitute
Show the diagram of the joint D as in Figure 4.
Here,
Refer to Figure 4.
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 AD
Substitute
Partially differentiate the expression for the force acting at member AB
Calculate the deflection of the member AB
Substitute
Partially differentiate the expression for the force acting at member AD
Calculate the deflection of the member AD
Substitute
Partially differentiate the expression for the force acting at member BD
Calculate the strain energy of the member BD
Substitute
Partially differentiate the expression for force acting at member BC
Calculate the strain energy of the member BC
Substitute
Partially differentiate the expression for force acting at member CD
Calculate the strain energy of the member CD
Substitute
Calculate the vertical deflection of joint B
Substitute
Substitute 0 for Q.
Hence, the horizontal deflection of joint B
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Chapter 11 Solutions
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