Concept explainers
Find the slope

Answer to Problem 33P
The slope
The deflection
The slope
The deflection
Explanation of Solution
Given information:
The Young’s modulus (E) is 29,000 ksi.
The moment of inertia (I) is
Calculation:
Consider flexural rigidity EI of the beam is constant.
Show the free body diagram of the given beam as in Figure (1).
Refer Figure (1),
Consider upward is force is positive and downward force is negative.
Consider clockwise moment is negative and counterclockwise moment is positive.
Split the given beam into two sections such as AC and CE.
Consider the portion CE:
Draw the free body diagram of the portion CE as in Figure (2).
Refer Figure (2),
Consider a reaction at C and take moment about point C.
Determine the reaction at E;
Determine the reaction at support A;
Show the reaction of the given beam as in Figure (3).
Refer Figure (3),
Determine the moment at A:
Determine the bending moment at B;
Determine the bending moment at C;
Determine the bending moment at D;
Determine the bending moment at E;
Show the
Show the elastic curve diagram as in Figure (5).
Refer Figure (4),
Determine the slope at B;
Here, b is the width and h is the height of respective triangle.
Substitute 12 ft for
Substitute 29,000 ksi for E and
Hence, the slope at B is
Determine the deflection between A and B using the relation;
Here,
Substitute 12 ft for
Substitute 29,000 ksi for E and
Hence, the deflection at B is
To determine the slope at point E, it is necessary to determine the deflection at point C and the deflection between C and E.
Determine the deflection at C and A using the relation;
Substitute 12 ft for
Determine the deflection between C and E using the relation;
Substitute 12 ft for
Determine the slope at E using the relation;
Here,
Substitute
Determine the slope between D and E using the relation;
Here, b is the width and h is the height of respective triangle.
Substitute 12 ft for
Determine the slope at D using the relation;
Substitute
Substitute 29,000 ksi for E and
Hence, the slope at D is
Determine the deflection between D and E using the relation;
Here, b is the width and h is the height of respective rectangle and triangle.
Substitute 12 ft for
Determine the deflection at D using the relation;
Substitute 12 ft for
Substitute 29,000 ksi for E and
Hence, the deflection at point D is
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Chapter 6 Solutions
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