Analysis Topic 4 Answer

Analysis Topic 4 Answer - Problem 4.4 Draw the ILs for the...

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CIVL2007 THEORY AND DESIGN OF STRUCTURES II DEPARTMENT OF CIVIL ENGINEERING THE UNIVERSITY OF HONG KONG TOPIC 4: INFLUENCE LINES FOR STATICALLY INDETERMINATE STRUCTURES - ANSWERS - Problem 4.2 Draw the ILs for the reactions at the supports and the shear and bending moment at point B of the following beam using the method of consistent deformation (confirm your answers using Müller Breslau’s Principle). Determine the IL ordinates at 5m intervals. Select the reaction at support C to be the redundant. (EI is constant) Influence line ordinates R C : 0 at A; 0.148 at B; 1 at C R A : 1 at A; 0.852 at B; 0 at C M A : 0 at A and C; 2.78 at B M B : 0 at A and C; 0.148 at B V B : 0 at A and C; -0.148 at B left ; 0.852 at B right Problem 4.3 Determine the ILs for Problem 4.2 for the reactions at the supports of the beam by selecting the moment at support A to be the redundant (use the method of consistent deformation to determine the ILs and IL ordinates at 5m intervals). See solution for 4.2 15m A C B 5 R C R A M B M A V B
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Unformatted text preview: Problem 4.4 Draw the ILs for the reactions at the supports and the shear and bending moment at point D of the following beam using the method of consistent deformation and Müller Breslau’s Principle. Determine the IL ordinates at 4m intervals. R A : 1 at A; 0 at B and D; -0.047 at C; 0.063 at E R B : 0 at A and D; 1 at B; 0.594 at C; -0.625 at E R D : 0 at A and B; 0.453 at C; 1 at D; 1.563 at E V C : 0 at A, B and D; -0.453 at C left , 0.547 at C right ; -0.563 at E M C : 0 at A, B and D; 1.81 at C; -1.75 at E Problem 4.5 Construct the influence lines for the moment at A and B and the shear at C for the frames shown below using the Müller Breslau Principle. Draw two different possible ILs for the shear at point C. Determine the location of uniformly distributed member loads to maximise the positive moment at A and shear at C using the IL. B A C 8 m A B C I (mm 4 ) D 4 4 4 E 3I C V C Note: the other IL solution for V C will have columns in double B M B A M A...
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Analysis Topic 4 Answer - Problem 4.4 Draw the ILs for the...

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