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Fundamentals of Structural Analysis Episode 1 Part 9

Tham khảo tài liệu 'fundamentals of structural analysis episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Beam and Frame Analysis Force Method Part III by S. T. Mau P beam Conjugate beam method to find Ab . The deflection is computed as the moment at b of the conjugate beam. Ab ZMb -4 t 5 41 Downward. EI 2 2 2 3 2 48EI 1 beam ôbb ZMb -4 4 L L 4 L Ậ Downward. EI 2 3 3EI Rb - - - P Upward. Ỳ ôbb 16 4 Find other reaction forces and draw the shear and moment diagrams. This is achieved through a series of diagrams in the figure below. 155 Beam and Frame Analysis Force Method Part III by S. T. Mau P 11P 16 3PL 16 L 2 L 2 b 5P 16 11P 16 ị---------------ị V 1--------------- -5P 16 M A -3PL 16 Reactions shear moment and deflection diagrams. Example 25. Find all reactions of the same beam as in Example 24 but choose a different redundant force. EI is constant. P b a L 2 L L 2 J Beam statically indeterminate to the first degree. Solution. There are different ways of establishing a primary structure. For example inserting a hinge connection at any point along the beam introduces one condition of construction and renders the resulting structure statically determinate. We now choose to put the hinge at the fixed end effectively selecting the end moment Ma as the redundant force. 156 Beam and Frame Analysis Force Method Part III by S. T. Mau Ma P L 2 L 2 b Primary structure and redundant moment Ma. The compatibility equation is established from the condition that the total rotation at a of the primary structure due to the combined effect of the applied load and the redundant force Ma must be zero which is required by the fixed end support. p Oa 0 M0a b Compatibility condition and principle of superposition. 0a 0 a Madaa 0 .