Shear and bending Moment Diagrams for Frames

Shear and bending Moment Diagrams for Frames
A frame is 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
design frames

Procedure for analysis

The following is a procedure for constructing the shear and moment diagrams for a frame

  1. Determine the support reactions for the frame, if possible.
  2. Determine the support reactions A, V, and M at the end of each member using the method of sections.
  3. Construct both shear and moment diagrams just as before.

We will use the following sign convention: always draw the moment diagram on the compression side of the member.

Practical Example

Draw the shear and moment diagrams for the following frame:
shear and moment diagrams
First, find as many external reactions as possible.
external reactions
Second, cut the frame into its component members and find the internal reactions
frame into its component members
Next, solve the equations of equilibrium for each member. Let’s start with member AB.
equations of equilibrium
Next, solve the equations of equilibrium for member CD.
equations of equilibrium
Now, let’s draw the shear and moment diagram (remember to draw the diagram on the compression side of the member).
shear and moment diagram
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