Concept explainers
Find the slope
Answer to Problem 60P
The slope
The deflection
The slope
The slope
The deflection
Explanation of Solution
Given information:
The Young’s modulus (E) is 30,000 ksi.
The moment of inertia of the section AB is (I) is
The moment of inertia of the section BD is (I) is
Calculation:
Consider flexural rigidity EI of the beam is constant.
To draw a
Show the free body diagram of the given beam as in Figure (1).
Refer Figure (1),
Consider upward is positive and downward is negative.
Consider clockwise is negative and counterclowise is positive.
Refer Figure (1),
Consider reaction at A and C as
Take moment about point B.
Determine the reaction at D;
Determine the reaction at support A;
Determine the moment at A:
Show the reaction of the given beam as in Figure (2).
Determine the bending moment at B;
Determine the bending moment at C;
Determine the bending moment at D;
Determine the positive bending moment at A using the relation;
Show the reaction and point load of the beam as in Figure (3).
Determine the value of
Substitute
Show the
Show the conjugate beam as in Figure (5).
Determine the support reaction at support B;
Determine the shear force at B (left) using the relation;
Substitute 16 ft for
Determine the slope at B (left) using the relation;
Substitute 30,000 ksi for E and
Hence, the slope at B (left) is
Determine the slope at B (right) using the relation;
Substitute
Substitute 30,000 ksi for E and
Hence, the deflection at B (right) is
Determine the bending moment at B using the relation;
Substitute 16 ft for
Determine the deflection at B using the relation;
Substitute 30,000 ksi for E and
Hence, the deflection at B is
Determine the shear force at D using the relation;
Here, b is the width and h is the height of respective triangle and parabola.
Substitute 16 ft for
Determine the slope at D using the relation;
Substitute 30,000 ksi for E and
Hence, the deflection at D is
Determine the bending moment at D using the relation;
Substitute 16 ft for
Determine the deflection at D using the relation;
Substitute 30,000 ksi for E and
Hence, the deflection at D is
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Chapter 6 Solutions
Structural Analysis, SI Edition