Explanation Write the condition for static instability, determinacy and indeterminacy of plane frames as follows: 3 m + r < 3 j + e c statically unstable frame (1) 3 m + r = 3 j + e c statically determinate frame (2) 3 m + r > 3 j + e c statically indeterminate frame (3) Here, number of members is m , number of external reactions is r , the number of joints is j , and the number of elastic hinges is e c . Find the degree of static indeterminacy ( i ) using the equation; i = ( 3 m + r ) − ( 3 j + e c ) (4) Refer to the Figure in the question; The number of members ( m ) is 2. The number of external reactions ( r ) is 3. The number of joints ( j ) is 3. The number of elastic hinges e c is 0. Substitute the values in Equation (2); 3 ( 2 ) + 3 = 3 ( 3 ) + 0 9 = 9 statically determinate frame Show the free-body diagram of the entire frame as in Figure 1. Find the vertical reaction at point C by taking moment about point A . + ↺ ∑ M A = 0 C y ( 15 ) − 2 ( 15 ) ( 15 2 ) − 20 ( 6 ) = 0 15 C y − 225 − 120 = 0 C y = 23 k ↑ Find the vertical reaction at point A by resolving the vertical component of forces. + ↑ ∑ F Y = 0 A y − 2 ( 15 ) + C y = 0 A y − 30 + 23 = 0 A y = 7 k ↑ Find the horizontal reaction at point A by resolving the horizontal component of forces. + → ∑ F X = 0 20 − A x = 0 A x = 20 k ← Show the free-body diagram of the members and joints of the entire frame as in Figure 2. Consider point A : Resolve the vertical component of forces. + ↑ ∑ F Y = 0 7 − A Y A B = 0 A Y A B = 7 k Resolve the horizontal component of forces. + → ∑ F X = 0 A X A B − 20 = 0 A X A B = 20 k Consider the member AB : Resolve the vertical component of forces. + ↑ ∑ F Y = 0 A Y A B + B Y A B = 0 7 + B Y A B = 0 B Y A B = − 7 k Resolve the horizontal component of forces. + → ∑ F X = 0 A X A B − B X A B + 20 = 0 20 − B X A B + 20 = 0 B X A B = 0 Take moment about the point B

6th Edition

ISBN: 9781337630931

Author: KASSIMALI, Aslam.

Publisher: Cengage,

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Chapter 5, Problem 58P

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Plot the shear diagram, bending moment diagram, axial force diagram, and the qualitative deflected shape of the frame.

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Plot the shear diagram, bending moment diagram, axial force diagram, and the qualitative deflected shape of the frame.

Solution Summary: The author explains the condition for static instability, determinacy, and indeterminity of plane frames.

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Plot the shear diagram, bending moment diagram, axial force diagram, and the qualitative deflected shape of the frame.

Chapter 5 Solutions