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 horizontal reaction at point A by resolving the horizontal component of forces. + → ∑ F X = 0 A x − 3 × 18.03 × 3 13 = 0 A x = 45 k → Find the resultant reaction at point A by taking moment about point C . + ↺ ∑ M C = 0 − A y ( 30 ) − 45 ( 15 ) + 45 ( 20 ) + 3 × 18.03 × 5 × 2 13 + 3 × 18.03 × 7.5 × 3 13 = 0 − 30 A y − 675 + 900 + 150.02 + 712.56 = 0 A y = 23.75 k ↑ Find the vertical reaction at point C by resolving the vertical component of forces. + ↑ ∑ F Y = 0 A y − 45 − 3 × 18.03 × 2 13 + C y = 0 23.75 − 45 − 30 + C y = 0 C y = 51.25 k ↑ Consider point C : Resolve the vertical component of forces. + ↗ ∑ F Y = 0 C ′ y = C y ( 2 13 ) = 51.25 ( 2 13 ) = 28.43 k ↗ Resolve the horizontal component of forces. + ↖ ∑ F X = 0 C ′ x = C y ( 3 13 ) = 51.25 ( 3 13 ) = 42.64 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 23.75 − A Y A B = 0 A Y A B = 23.75 k Resolve the horizontal component of forces. + → ∑ F X = 0 45 − A X A B = 0 A X A B = 45 k Consider the member AB : Resolve the vertical component of forces

6th Edition

ISBN: 9781337630931

Author: KASSIMALI, Aslam.

Publisher: Cengage,

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Chapter 5, Problem 61P

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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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