Concept explainers
Find the slope
Answer to Problem 34P
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 Young’s modulus (E) 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 C;
Determine the reaction at support A;
Determine the moment at A:
Show the reactions 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;
Show the reaction and point load of the beam as in Figure (3).
Determine the value of
Substitute
Show the
Show the elastic curve as in Figure (5).
The slope at point B can be calculated by evaluating the change in slope between A and B.
Express the change in slope using the first moment-area theorem as follows:
Here, b is the width and h is the height of the respective triangle and rectangle.
Substitute 16 ft for
Determine the slope B (left) using the relation;
Substitute 30,000 ksi for E and
Hence, the slope at B (left) is
Determine the deflection at B using the relation;
Substitute
Determine the deflection at B (left) using the relation;
Substitute 30,000 ksi for E and
Hence, the deflection at B (left) is
Determine the deflection between B and C using the relation;
Here, b is the width and h is the height of the triangle.
Substitute 8 ft for b and
Express the relationship between the deflection and slope of span BC as follows:
Here,
Substitute
Determine the slope between B and C using the relation;
Substitute 8 ft for b and
Determine the slope at B (right) using the relation;
Substitute
Substitute 30,000 ksi for E and
Hence, the slope at B (right) is
Determine the slope between C and D using the relation;
Here, b is the width and h is the height of the triangle.
Substitute 8 ft for b and
Determine the slope at D using the relation;
Substitute
Substitute 30,000 ksi for E and
Hence, the slope at point D is
Determine the deflection between C and D using the relation;
Substitute
Determine the deflection at point D using the relation;
Substitute 8 ft for
Substitute 30,000 ksi for E and
Hence, the deflection at point D is
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