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 equilibrium equations for forces acting on 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 connecting the 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.
Method of Joints
Joint A Joint B
Method of Joints
Upper chord members Verticals
Tension Force
Joint A
Joint B
Diagonals
Lower chord members
Compression Force
Method of Joints
gusset plate weld
Method of Joints
Upper chord in compression
Idealized joint members connected by a frictionless pin
Lower chord in tension This is a Pratt truss
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. If possible, determine the support reactions 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).
Lower chord in tension This is a Howe truss
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.
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
MA 0 F
10 ft
500 lb(10ft ) Cy (10ft ) 500 lb
500 lb
Cy = 500 lb
10 ft Ax
0 Ay Cy 0 Ax 500 lb
Ay = -500 lb Ax = -500 lb
Ax
10 ft
Ay
Cy
10 ft
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
Method of Joints
The equations of equilibrium for Joint B
500 lb
0 FBC cos 45 500 lb
FAC
0 FAC 500 lb 0 FAB 500 lb
FAC = 500 lb FAB = 500 lb
FBC FAB
FBC = -707.2 lb
500 lb
The forces in the truss can be summarized as: FAB = 500 lb (T) FAC = 500 lb (T) FBC = 707.2 lb (C)
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
E A
60
4 ft 4 ft
60
800 lb
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 loading changes. Zeroforce members may be determined by inspection of the joints
CIVL 3121
Trusses - Method of Joints
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Zero Force Members
Case 1: If two members are connected at a joint and there is no external force applied to the joint
y F1
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
F F
0 F1 sin 0 F1 cos F2
F1 = 0
F2 = 0
F3
F2 x
F2 x
0 F1 sin
F1 = 0
Zero Force Members
Determine the force in each member of the truss shown below:
800 lb
Zero Force Members
Determine the force in each member of the truss shown below:
800 lb
Using Case 2 FBG and FDF are zero-force members
B
Using Case 1 FAG and FCG are zero-force members
B
Using Case 1 FEF and FCF are zero-force members
D E G F
D E G F
8 ft
8 ft
8 ft
8 ft
Zero Force Members
Determine the force in each member of the truss shown below:
The remaining non-zero forces can be found using the method of joints
800 lb
3
Method of Joints
The equations of equilibrium for Joint C
800 lb
F
FCD
0 FBC FCD
3 5 3 5
4 3
4 5
4 5
FBC = FCD
C FBC
0 FBC FCD 800 lb
D E G F
FBC = -666.7 lb FBC = 666.7 lb (C)
8 ft
8 ft
CIVL 3121
Trusses - Method of Joints
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End of Trusses - Part 2
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