Each term is accompanied by a brief definition.
Then we can solve those equations simultaneously to find the end rotations. These end rotations may then be substituted back into the slope-deflection equations to find the real moments at the ends of all of the members. From these moments, we can find the shears and reactions and the moment diagrams for the entire structure.
The entire process for an indeterminate beam is summarized as follows: Find all of the unrestrained DOFs in the beam structure. Define an equilibrium condition for each DOF for rotations, the sum of all moments at each rotating node must equal zero.
Construct each slope deflection equation. Use the resulting equilibrium equations to solve for the values or the unknown DOF rotations solving a system of equations.
Use the now-known DOF rotations to find the real end moments for each element of the beam sub the rotations back into the slope-deflection equations. Use the end moments and external loadings to find the shears and reactions.
Draw the resultant shear and bending moment diagrams. Node B cannot move horizontally since it is restrained by members AB and BC, which are both fixed horizontally.
Node B is also restrained from moving vertically due to the roller support at that location; however, node B can rotate.
Overall, this structure has only one DOF, which means it is a good structure to analyse using the slope-deflection method. For the sole rotational DOF at node B, the equilibrium condition will be: These two moments are the only moments that act at point B.
For equilibrium to be maintained the sum of the moments around node B must sum to zero. The next step is to construct the slope-deflection equations for each member to find an expression for the moment at each end in terms of the end rotations, chord rotation, and fixed end moments.
There are two slope deflection equations for each member one for the moment at each end. We first need to find the chord rotations and fixed end moments for both members, since they are a required input for the slope-deflection equations. This results in a rotation of the chord of the member.
Recall that the element chord is just a straight line that joins the two ends of the member without regard to the actual deflected shape of the beam, as shown in the figure.The Slope-Deflection method is an alternative formulation of the displacement method which is also known as the stiffness method, the slope deflection method deals only with the .
© regardbouddhiste.com 1 MECHANICS OF SOLIDS - BEAMS TUTORIAL 3 THE DEFLECTION OF BEAMS This is the third tutorial on the bending of beams.
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The procedure to compute a deflection component Apply a unit couple at the point where slope is to computed A D BC x P (real load) L Deflections Let’s examine the following beam and use virtual work to Using the method of section the virtual moment expressions are: ft.
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– Determine the deflection of statically determinate beam by using Macaulay’s Method. • Expected Outcomes: – Able to analyze determinate beam – deflection and slope by Macaulay Method. Slope-Deflection Method Updated February 20, Page 4 Interpretation of the Slope-Deflection Equation Several insights are gained from the slope-deflection equation, and these insights.