Explanation Given: The supports A and C are fixed. B is roller support in a rigid base. The girder has thickness of 4 ft . Concept Used: Write the expression for fixed end moments. F E M = coefficients × w L 2 .......(I) Here, uniform distributed load is w and length of the span is L . Write the expression for the absolute stiffness factor for member B A . K B A = k B A E I L .......(II) Here, the absolute stiffness factor of the member BA is K B A , stiffness factor for member B A is k B A . moment of inertia is I , modulus of elasticity is E and length of the span is L . Write the expression for the absolute stiffness factor for member A B . K A B = k A B E I L .......(III) Here, stiffness factor for member A B is k A B . Write the expression for absolute stiffness factor for member B C . K B C = k B C E I L .......(IV) Here, stiffness factor for member B C is k B C . Write the expression for absolute stiffness factor for member C B . K C B = k C B E I L .......(V) Here, stiffness factor for member C B is k C B . Write the expression for slope deflection equation. M N = K N ( θ N + C N θ F − ψ ( 1 + C N ) ) + ( F E M ) N .......(VI) Here, internal moment at the near end of the span is M N , absolute stiffness of the near end is K N , near end slope of the span at the support is θ N , far end slope of the span at the support is θ F and the span cord rotation due to a linear displacement. Calculation: The diagram of the beam is shown below. Figure (1) Consider Figure (1). Length of span is L = 20 ft . Length of haunch at end A is 6 ft . Length of haunch at end B is 4 ft . Calculate ratio of length of haunch at end A to the length of the span A B . a A = 6 ft 20 ft = 0.3 Calculate ratio of length of haunch at end B to the length of the span A B . a B = 4 ft 20 ft = 0.2 Calculate ratio for rectangular cross-sectional area at end A . r A = 4 ft − 2 ft 2 ft = 1 Calculate ratio for rectangular cross-sectional area at end B . r B = 4 ft − 2 ft 2 ft = 1 Calculate ratio of length of haunch at end B to the length of the span A B . a B = 4 ft 20 ft = 0.2 Calculate ratio of length of haunch at end C to the length of the span B C . a C = 6 ft 20 ft = 0.3 Calculate ratio for rectangular cross-sectional area at end B . r B = 4 ft − 2 ft 2 ft = 1 Calculate ratio for rectangular cross-sectional area at end C . r C = 4 ft − 2 ft 2 ft = 1 Determine carry over factor of member A B at end A from straight haunches-constant width table and ratios calculated. C A B = 0.622 Determine carry over factor of member A B at end B from straight haunches-constant width table and ratios calculated. C B A = 0.748 Determine carry over factor of member B C at end B from straight haunches-constant width table and ratios calculated. C B C = 0.748 Determine carry over factor of member B C at end C from straight haunches-constant width table and ratios calculated. C C B = 0.622 Determine stiffness factor of member A B at end A from straight haunches-constant width table and ratios calculated. k A B = 10.06 Determine stiffness factor of member A B at end B from straight haunches-constant width table and ratios calculated. k B A = 8.37 Determine stiffness factor of member B C at end B from straight haunches-constant width table and ratios calculated. k B C = 8.37 Determine stiffness factor of member B C at end C from straight haunches-constant width table and ratios calculated. k C B = 10.06 Calculate absolute stiffness factor for member B A . Substitute 8.37 for k B A and 20 ft for L in Equation (II). K B A = ( 8.37 ) E I 20 ft = 0.41875 E I Calculate absolute stiffness factor for member A B . Substitute 10.06 for k A B and 20 ft for L in Equation (III). K A B = ( 10.06 ) E I 20 ft = 0.503 E I Calculate absolute stiffness factor for member B C . Substitute 8.37 for k B C and 20 ft for L in Equation (IV). K B C = ( 8.37 ) E I 20 m = 0.418 E I Calculate absolute stiffness factor for member C B . Substitute 10.06 for k C B and 20 ft for L in Equation (V). K C B = ( 10.06 ) E I 20 ft = 0.503 E I Calculate fixed end moment for member A B . Determine coefficients from straight haunches-constant width table. Substitute 8 k/ft for w , − 0.1089 for coefficient and 20 ft for L in Equation (I). ( F E M ) A B = ( − 0.1089 ) × ( 8 k/ft ) ( 20 ft ) 2 = − 348.48 k-ft Calculate fixed end moment for member B A . Determine coefficients from straight haunches-constant width table. Substitute 8 k/ft for w , 0

Structural Analysis, Student Value Edition

10th Edition

ISBN: 9780134622088

Author: HIBBELER, Russell C.

Publisher: PEARSON

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Matrix Algebra for Structural analysis

Structural analysis is a process in which the effects of different loads and internal forces, acting on structures and their elements are determined. This method of analysis is effective in detecting the failure loads of the structural elements and the d…

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Chapter 13, Problem 13.2P

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The moment about points A, B and C.

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Chapter 13 Solutions

Structural Analysis, Student Value Edition

Ch. 13 - Prob. 13.1P Ch. 13 - Prob. 13.2P Ch. 13 - Prob. 13.3P Ch. 13 - Prob. 13.4P Ch. 13 - Prob. 13.5P Ch. 13 - Prob. 13.6P Ch. 13 - Prob. 13.7P Ch. 13 - Prob. 13.8P Ch. 13 - Prob. 13.9P Ch. 13 - Prob. 13.10P

Ch. 13 - Prob. 13.11P Ch. 13 - Prob. 13.12P

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