Draw the influence lines for (a) the moment at C, (b) the vertical reaction at A, and (c) the shear at C. Assume A is a fixed support. Solve this problem using the basic method of Sec. 6.1.
(a)
The influence lines for the moment at
Answer to Problem 6.1P
The influence line for the moment at
Explanation of Solution
Concept Used:
The unit load as
Calculation:
The following figure shows the free body diagram of the beam.
Figure-(1)
Write the equilibrium equation for the moment about point
Here, the net moment about the point
When the point load is at
Substitute,
When the point load is at
Substitute,
Conclusion:
According to the value of
Figure-(2)
(b)
The influence line for the vertical reaction at
Answer to Problem 6.1P
The influence line for the vertical reaction at
Explanation of Solution
Concept Used:
The unit load as
Calculation:
The following figure shows the free body diagram of the beam.
Figure-(3)
Write the equilibrium equation for the forces acting in the vertical direction.
Here, summation of the vertical forces is
Conclusion:
According to the value of the vertical reaction at
Figure-(4)
(c)
The influence line for the shear at
Answer to Problem 6.1P
The influence line for the shear at
Explanation of Solution
Concept Used:
The unit load as
Calculation:
Consider the right segment of the beam as shown in Figure-(5).
Figure-(5)
Write the equilibrium equation for the forces acting in the vertical direction.
Here, summation of the vertical forces is
Now, consider the left segment of the beam as shown in Figure-(6).
Figure-(6)
Write the equilibrium equation for the forces acting in the vertical direction.
Conclusion:
According to the values of
Figure-(7)
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