Shear and Moment Diagrams for Frames - …

1 Shear and Moment Diagrams for Frames A frameis a structure composed of several members that are either fixed or pin connected at their ends. It is often necessary to draw Shear and Moment Diagrams to design Frames . Shear and Moment Diagrams for FramesProcedure for analysis- the following is a procedure for constructing the Shear and Moment Diagrams for a frame the support reactions for the frame , if the support reactions A, V, and Mat the end of each member using the method of both Shear and Moment Diagrams just as will use the following sign convention: always draw the Moment diagram on the compression side of the and Moment Diagrams for FramesExample.

2 Draw the Shear and Moment Diagrams for the following and Moment Diagrams for FramesFirst, find as many external reactions as k0AM 016kyyyFAD (8 ft.) 16k(10 ft.)(20 ft.)yD Ay= kDy= Ax= kShear and Moment Diagrams for FramesSecond, cut the frame into its component members and find the internal k16 k k16 and Moment Diagrams for FramesNext, solve the equations of equilibrium for each member. Let s start with member AB. k k16 (8 ft.) k(16 ft.)BBMM By= kMB= k Bx= 0 CIVL 3121 Shear Force and Bending Moment Diagrams for Frames1/4 Shear and Moment Diagrams for FramesNext, solve the equations of equilibrium for member CD.

3 0 CCMM Cy= kMC= 00 xxFCCx= k16 and Moment Diagrams for FramesNow, let s draw the Shear and Moment diagram (remember to draw the diagram on the compression side of the member). Shear DiagramdVwdx ( ) ( ) k k k and Moment Diagrams for FramesExample: Draw the Shear and Moment Diagrams for the following frame :3 k4 and Moment Diagrams for FramesExample: Draw the Shear and Moment Diagrams for the following frame : Shear and Moment Diagrams for FramesExample: Draw the Shear and Moment Diagrams for the following frame : Shear and Moment Diagrams for FramesExample: Draw the Shear and Moment Diagrams for the following frame .

4 4 k4 3121 Shear Force and Bending Moment Diagrams for Frames2/4 Shear and Moment Diagramsby Superposition We have learned how to construct a Moment diagram from either writing the Moment as a function of xor from the slope relationship with the Shear diagram. If the beam or frame is linearly elastic, we can use the principles of superposition to construct Moment Diagrams from a series of parts rather than from a single complex shape. Shear and Moment Diagramsby SuperpositionMost loadings on beams and Frames in structural analysis can be formed as a combination of the following loadings:xV(k)PxM(k ft.)

5 LPxV(k)xM(k ft.)LM0 Shear and Moment Diagramsby SuperpositionMost loadings on beams and Frames in structural analysis can be formed as a combination of the following loadings:Lw0xV(k)xM(k ft.)02wL203wLxV(k)Lw0xM(k ft.)0wL202wLShear and Moment Diagramsby SuperpositionExample: Draw the Shear and Moment Diagrams for the following beam using k10 and Moment Diagramsby SuperpositionThe Shear Diagrams using superposition10 k10 k+xV(k)50xV(k)10xV(k)6010 Shear and Moment Diagramsby SuperpositionThe Moment Diagrams using superposition10 k10 k+xM(k ft.)

6 -200xM(k ft.)-250xM(k ft.)-450 CIVL 3121 Shear Force and Bending Moment Diagrams for Frames3/4 Shear and Moment Diagramsby SuperpositionExample: Draw the Shear and Moment Diagrams for the following beam using superposition: Shear and Moment Diagramsby SuperpositionExample: Draw the Shear and Moment Diagrams for the following beam using superposition:++= Shear and Moment Diagramsby SuperpositionExample: Draw the Shear and Moment Diagrams for the following beam using superposition:++= Shear and Moment Diagramsby SuperpositionExample: Draw the Shear and Moment Diagrams for the following beam using k of Internal Loads Part 4 Any questions?

7 CIVL 3121 Shear Force and Bending Moment Diagrams for Frames4/4