Concept explainers
Find the equations for slope and deflection of the beam using direct integration method.
Answer to Problem 1P
The equation for slope is
The equation for deflection is
Explanation of Solution
Calculation:
Consider the flexural rigidity EI of the beam is constant.
Draw the free body diagram of the beam as in Figure (1).
Refer Figure (1),
Find the reaction at support B.
Find the reaction at support A.
Draw the section at x distance from support A as in Figure (2).
Refer Figure (2),
Write the equation for bending moment at x distance.
Write the equation for
Integrate Equation (1) to find the equation of the slope.
Integrate Equation (2) to find the equation of the deflection.
Find the integration constants
Apply boundary conditions in Equation (3):
At x=0 and y=0.
At x=L and y=0.
Find the equation of the slope.
Substitute
Thus, the equation of the slope is
Find the equation of the deflection.
Substitute
Thus, the equation of the deflection is
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Structural Analysis