Flexibility Method: Beams and Frames with more than one redundant, and a Truss withone redundant.Solve the following 3 problems:Problem 1:Given: The following beam has fixed supports at A and B, and has a constant EI.WRequired:Evaluate the two vertical reactions (Ay and By) and the two moment reactions (MA andMB). Neglect Ax and Bx.Draw the Shear DiagramDraw the Moment DiagramSketch the deflected shapeHint: In this problem, it looks like it is indeterminate to the third degree, but let's neglect axialeffects. By neglecting axial effects, we are not considering the horizontal force equilibriumequation (i.e., we neglect sum of fores in the x-direction). Thus, we neglect the two horizontalreactions (Ax and Bx). Therefore, the problem simplifies as follows:We are left with 2 equilibrium equations (i.e., sum of forces in the y-direction and sum ofmoments). So, you have 2 equations and 4 unknowns: Ay, MA, By, and MB. Thus, we need tocome up with 2 more equations..these are your compatibility equations! In the end, you'llneed to consider two redundants.For this problem, please consider the following redundants:(1) the moment at B [MB] and(2) the vertical reaction at B [By].Doknow what the primary structure will look like? It will be a cantilever! You will need 3youdiagrams (Primary 0: primary structure with original loads; Primary 1: the primary structure witha unit VERTICAL force at B-assume downward; and Primary 2: the primary structure with aunit MOMENT at B-assumed clockwise. Each of the 3 diagrams will have a verticaldeflection (movement 1) and a rotation (movement 2) at the cantilever tip. Note: you will have abig delta (A10) and a big theta (020).You may use the formula sheet in the notes Appendix to compute all the coefficients. UseMaxwell's Theorem of Reciprocal Deflections where appropriate.

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Problem 1: Given: The following beam has fixed supports at A and B, and has a constant EI. A. Required: Evaluate the two vertical reactions (Ay and By) and the two moment reactions (MA and MB). Neglect Ax and Bx. Draw the Shear Diagram Draw the Moment Diagram Sketch the deflected shape

Problem 1: Given: The following beam has fixed supports at A and B, and has a constant EI. A. Required: Evaluate the two vertical reactions (Ay and By) and the two moment reactions (MA and MB). Neglect Ax and Bx. Draw the Shear Diagram Draw the Moment Diagram Sketch the deflected shape

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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