Shear and Moment Diagrams for Frames - Procedure for analysis

Oct 25, 2026

Uploaded by Connor

Shear and moment diagrams for frames are constructed to support structural design. The material defines a frame as a set of members fixed or pinned at their ends and explains why shear and moment diagrams are needed. A step-by-step procedure covers determining support reactions, finding end reactions for each member by the method of sections, and then building shear and moment diagrams using a stated sign convention on the compression side.

LanguageEnglish

CategoryTechnology

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Pages5

Reading Time13 min

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Shear and Moment Diagrams for Frames

Procedure for analysis

Sign convention and equilibrium

Shear and Moment Diagrams by Superposition

Constructing diagrams for combined loadings

| Shear and 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. | | | Shear and Moment Diagrams for Frames | | | | --- | --- | --- | | Example: Draw the shear and moment diagrams for the following frame:
0.8 k/ft. | | | | 0.6 k/ft. | | 16 ft. | | Shear and Moment Diagrams for Frames | | | | | | --- | --- | --- | --- | --- | | Second, cut the frame into its component members and find the internal reactions | | | | | |
MB

Bx
0.6 k/ft.
9.6 k 4.16 k | 16 k | 0.8 k/ft. | | Cy
Cx

MC
16 ft.
11.84 k | | | | | Mc

Cx | | Shear and Moment Diagrams for 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. | Shear and Moment Diagrams for Frames | | | --- | --- | | First, find as many external reactions as possible. | | | 16 k
0.8 k/ft.
0.6 k/ft
9.6 k

16 ft.
Dy | 􀀴􀀎 􀂦 MA 􀀠 0
􀀠 􀀐9.6k(8 ft.) 􀀐 16k(10 ft.) 􀀎 Dy (20 ft.)
Dy = 11.84 k
􀀎 􀁮 􀂦 Fy 􀀠 0 􀀠 Ay 􀀎 Dy 􀀐 16k
Ay = 4.16 k
􀀎􀁯 􀂦 Fx 􀀠 0 􀀠 Ax 􀀎 9.6k
Ax = -9.6 k | | Shear and Moment Diagrams for Frames | | | --- | --- | | Next, let’s start with a FBD that we can complete solve. In this example it would be either AB or CD. | | | | 16 k
0.8 k/ft. Cy
| | Shear and Moment Diagrams for Frames | | | --- | --- | | Let’s start with member AB. | | | | 16 k
0.8 k/ft. Cy
| | Shear and Moment Diagrams for Frames | | | --- | --- | | Next, solve the equations of equilibrium for member CD. | | | Cy
Cx

MC
16 ft.
11.84 k | 􀀴􀀎 􀂦 MC 􀀠 0 􀀠 􀀐MC MC = 0
􀀎 􀁮 􀂦 Fy 􀀠 0 􀀠 11.84k 􀀐 Cy Cy = 11.84 k
􀀎􀁯 􀂦 Fx 􀀠 0 􀀠 􀀐Cx Cx = 0

| | Shear and Moment Diagrams for Frames | | | --- | --- | | Example: Draw the shear and moment diagrams for the following frame: | | | 3 k/ft. | 4 ft.
15 k
4 ft.
| | Shear and Moment Diagrams for Frames | | | | | --- | --- | --- | --- | | Let’s start with member AB. | | | | | MB

By

0.6 k/ft.
9.6 k 4.16 k | 􀀴􀀎 􀂦 MB 􀀠0 􀀠 MB 􀀎 9.6k(8 ft.) 􀀐 9.6k(16 ft.) | | | | | 􀀎 􀁮 􀂦 Fy | 􀀠 0 􀀠 4.16k 􀀎 By | | | | 􀀎􀁯 􀂦 Fx 􀀠 0 􀀠 Bx 􀀐 9 .6k 􀀎 9.6k
Bx = 0 | | | | Shear and Moment Diagrams for Frames | | | --- | --- | | Now, let’s draw the shear and moment diagram (remember to draw the diagram on the compression side of the member) . | | | Shear Diagram | Moment Diagram

87.6 k ft.
76.8 k ft.
76.8 k ft. | |
dV
dx
􀀠 􀀐w
4.16 k
V(x) 􀀠 4. 16 􀀐 0 .8x
V(x) 􀀠 4. 16 􀀐 0 .8x 􀀠 0
x 􀀠
4.16 0.8
􀀠 5.2 ft.
11.84 k
9.6 k | | Shear and Moment Diagrams for Frames Example: Draw the shear and moment diagrams for the following frame: Shear and Moment Diagrams for Frames Example: Draw the shear and moment diagrams for the following frame: Shear and Moment Diagrams for Frames End of Part 1 Any questions? | Shear and Moment Diagrams by Superposition | | | --- | --- | | Most loadings on beams and frames in structural analysis can be formed as a combination of the following loadings: | | | P

| M0

V

(k) ~~ ~~ x
M
(k ft.) ~~ ~~ x

L | Shear and Moment Diagrams for Frames Example: Draw the shear and moment diagrams for the following frame: Shear and Moment Diagrams by Superposition 􀂾 We have learned how to construct a moment diagram from either writing the moment as a function of x or from the slope relationship with the shear diagram. 􀂾 If t

FAQs

Why are shear and moment diagrams necessary for frame design?

They are used to design frames by revealing how internal shear and bending moments vary along members under loading.

What is the procedure to construct shear and moment diagrams for a frame?

Determine support reactions, then determine the end reactions for each member using the method of sections, and finally construct the shear and moment diagrams following the same approach as before.

How does the sign convention affect the moment diagram construction?

The moment diagram must always be drawn on the compression side of the member.

How does superposition help in drawing shear and moment diagrams?

For linearly elastic beams or frames, superposition allows moment diagrams to be built from multiple simpler parts rather than from one complex loading shape.

Oct 25, 2026

Uploaded by Connor