Slope of a Beam: Slope at any section in a deflected beam is defined as the angle in radians which the tangent at the section makes with the. Deflections and Slopes of Beams. TABLE G-1 DEFLECTIONS AND SLOPES OF CANTILEVER BEAMS. O DA y = deflection in the y direction (positive upward). a) Determine the deflection and slope at specific points on beams and shafts, centroid of each cross-sectional area of the beam is called the elastic curve.


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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 deflections and slopes of beams 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. Deflections and slopes of beams 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.

The Slope-Deflection Method for Beams |

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 deflections and slopes of beams a good structure to analyse using the slope-deflection method. Computer-aided Deflection and Slope Analyses of Beams.

Journal of Applied Sciences, 6: So the studies of material and structure are important.

Fortunately, the relations between behaviors, material and structure have been carried out by engineers, and written in some literatures[]. They are the exact forms. However, it is a troublesome computation process and easy to mistake.

Therefore, we have to develop some general algorithms and design an auto-analysis program to help us to accomplish these works. This study systematically and modularly combines the theories of solid mechanics, superposition, coordinate transformation, functional mapping and computer techniques[], etc.


With the help of this program, it is found that a great advantage, in deflections and slopes of beams and solving the solutions, is obtained; the necessary values of deflection and slope will be determined quickly and correctly from this program. We have two basic types of beams called cantilever and simply supported beams can be applied to construct the structures.

Beam Deflection Tables | MechaniCalc

There were some principles and formulas to describe the relations of deflection and slope for these beams. In this study, we take six necessary fundamental types and apply the superposition method to extend to any complex situations of forced beams.

Superposition method applied to multiple and non-standard forced beams Table 1 show the lists the six necessary deflections and slopes of beams types and graphs of forced beams and their deflection and slope equations.

Using the six fundamental types of forced beams, we can superpose any complex cases of multiple and non-standard forced beams as shown in Fig. These combinations can be finished just deflections and slopes of beams the six fundamental formulas provided in Table 1.