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CIVL 3121

Trusses - Method of Joints

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Method of Joints

If a truss is in equilibrium, then each of its joints must be in equilibrium. The method of joints consists of satisfying the th equilibrium equations for forces acting on ilib i ti f f ti each joint.

Method of Joints

Recall, that the line of action of a force acting on a joint is determined by the geometry of the truss member. The line of action is formed by c nnectin the f acti n f rmed connecting two ends of each member with a straight line. Since direction of the force is known, the remaining unknown is the magnitude of the force.

Fx

0

Fy

0

Method of Joints

Joint A Joint B

Method of Joints

Verticals Upper chord members

Tension Force

Joint A

Joint B

Diagonals

Lower chord members

Compression Force

Method of Joints

Method of Joints

Upper chord in compression

gusset plate

weld

Idealized joint members connected by a frictionless pin

Lower chord in tension

CIVL 3121

Trusses - Method of Joints

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Method of Joints

Upper chord in compression

Method of Joints

Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:

1. 1 If possible determine the support reactions possible,

Lower chord in tension

2. Draw the free body diagram for each joint. In general, assume all the force member reactions are tension (this is not a rule, however, it is helpful in keeping track of tension and compression members).

Method of Joints

Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:

3. Write the equations of equilibrium for each joint,

Method of Joints

Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:

4. If possible, begin solving the equilibrium equations at a joint where only two unknown reactions exist. Work your way from joint to joint, selecting the new joint using the criterion of two unknown reactions. 5. Solve the joint equations of equilibrium simultaneously, typically using a computer or an advanced calculator.

Fx

0

Fy

0

Method of Joints

Example - Consider the following truss

First, determine the support reactions for the truss 500 lb 500 lb

Method of Joints

Example - Consider the following truss

First, determine the support reactions for the truss

(10 lb MA 0 500 lb500 ft ) C y (10ft )

Cy = 500 lb

500 lb

10 ft Ax

Fy

Ay Cy

0 Ay C y 0 Ax 500 lb

10 ft

Ay = -500 lb

10 ft

Ax

10 ft

Fx

Ax = -500 lb

Ay

Cy

CIVL 3121

Trusses - Method of Joints

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Method of Joints

The equations of equilibrium for Joint A

FAB 500 lb FAC

Method of Joints

The equations of equilibrium for Joint B

500 lb

Fx

0 FBC cos 45 500 lb

Fx Fy

0 FAC 500 lb 0 FAB 500 lb

FAC = 500 lb FAB = 500 lb

FAB

FBC

FBC = -707.2 lb 707.2

The forces in the truss can be summarized as: FAB = 500 lb (T) FAC = 500 lb (T) FBC = 707.2 lb (C)

500 lb

Method of Joints

Problem Determine the force in each member of the truss shown below

Method of Joints

Problem Determine the force in each member of the truss shown below

B 4 ft C

A

60

4 ft

E

60

D

4 ft 800 lb

In the notes on page 10

Method of Joints

Problem Determine the force in each member of the truss shown below

Zero Force Members

Truss analysis may be simplified by determining members with no loading or zeroforce. These members may provide stability or be useful if the l di th loading changes. h Zeroforce members may be determined by inspection of the joints

CIVL 3121

Trusses - Method of Joints

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Zero Force Members

y

Zero Force Members

Case 2: If three members are connected at a joint and there is no external force applied to the joint and two of the members are colinear

y F1

Case 1: If two members are connected at a joint and there is no external force applied to the joint

F1

Fy Fx

0 F1 sin 0 F1 cos F2

F1 = 0 F2 = 0

F3

0 F1 sin

F2 x

F2 x

Fy

F1 = 0

Zero Force Members

Determine the force in each member of the truss shown below:

800 lb C

Zero Force Members

Determine the force in each member of the truss shown below:

800 lb C

In the notes on page 11

Using Case 1 FAG and FCG g G G are zero-force members

D E B

Using Case 2 FBG and FDF g are zero-force members

B

Using Case 1 FEF and FCF are zero-force members zero force

D E G F

A G F

A

8 ft

8 ft

8 ft

8 ft

Zero Force Members

Determine the force in each member of the truss shown below:

800 lb C FBC B D E G F

3

Method of Joints

The equations of equilibrium for Joint C

800 lb

4 4 3

The remaining non-zero forces can be found using the th method of joints th d f j i t

Fx

FCD

0 FBC FCD

3 5 3 5

4 5

4 5

FBC = FCD

Fy

0 FBC FCD 800 lb

FBC = -666.7 lb FBC = 666.7 lb (C)

A

8 ft

8 ft

CIVL 3121

Trusses - Method of Joints

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End of Trusses - Part 2

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