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 4. The number of external reactions ( r ) is 3. The number of joints ( j ) is 5. The number of elastic hinges e c is 0. Substitute the values in Equation (2); 3 ( 4 ) + 3 = 3 ( 5 ) + 0 15 = 15 statically determinate frame Show the free-body diagram of the entire frame as in Figure 1. Refer Figure 1, Find the vertical reaction at point B by taking moment about point A . + ↺ ∑ M A = 0 B y ( 10 ) − 15 ( 15 ) ( 15 2 ) − 12 ( 9 ) ( 9 2 ) = 0 10 B y − 1687.5 − 486 = 0 B y = 217.35 kN ↑ Find the vertical reaction at point A by resolving the vertical component of forces. + ↑ ∑ F y = 0 A y − 15 ( 15 ) + B y = 0 A y − 225 + 217.35 = 0 A y = 7.65 kN ↑ Find the horizontal reaction at point A by resolving the horizontal component of forces. + → ∑ F x = 0 − A x + 12 ( 9 ) = 0 A x = 108 kN ← 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 7.65 − A Y A C = 0 A Y A C = 7.65 kN Resolve the horizontal component of forces. + → ∑ F X = 0 − 108 + A X A C = 0 A X A C = 108 kN Consider the member AC : Resolve the vertical component of forces. + ↑ ∑ F Y = 0 A Y A C − C Y A C = 0 7

6th Edition

ISBN: 9781337630931

Author: KASSIMALI, Aslam.

Publisher: Cengage,

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Frames

The trusses and frames are the two most important structural members of civil engineering. Trusses are the interconnection of links and other structural members. The interconnection with other members makes the system behave as a single member that suppo…

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Chapter 5, Problem 65P

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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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Chapter 5, Problem 64P

Chapter 5, Problem 66P

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