Concept explainers
Bar ABC is fixed at both ends (see figure) and has load P applied at B. Find reactions at A and C and displacement SBif P = 200 kN. L = 2 m, t = 20 mm, b, = 100 mm, b2= 115 mm, and E = 96 GPa.
The reaction force at point A and C and displacement at point B.
Answer to Problem 2.4.8P
The reaction force at point A is
The reaction force at point C is
The displacement at point B is
Explanation of Solution
Given:
Load at point B is
The below figure shows the free body diagram of the bar.
Figure-(1)
Here, the reaction force at point A is
Write the expression for the force balance in horizontal direction.
Write the expression for the total deflection.
Here, the deflection of the section AB is
Write the expression for the deflection for section AB.
Here, the cross-section area is
Write the expression for the cross-section area of the bar AB.
Here, the width of the bar at point A is
Write the expression for the deflection for section AB.
Substitute
Write the expression for the cross-section area of the bar BC.
Here, the width of the bar at point C is
Write the expression for the deflection for section BC.
Substitute
Substitute
Substitute
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
The reaction force at point A is
The reaction force at point C is
The displacement at point B is
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Chapter 2 Solutions
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