1. Trusses
Lecture 7
Truss: is a structure composed of slender members (two-force members) joined together at their end points to support stationary or moving load.
Each member of a truss is usually of uniform cross section along its length.
Calculation are usually based on following assumption:
The loads and reactions act only at the joint.
Weight of the individual members can be neglected.
Members are either under tension or compression.
Joints: are usually formed by bolting or welding the members to a common plate, called a gusset plate, or simply passing a large bolt through each member.
Joints are modeled by smooth pin connections.

2. To find the reaction forces To find the force in each member
Analysis of Trusses
Lecture 7
Truss Analysis
External equilibrium
Internal equilibrium
To find the reaction forces
To find the force in each member
Method of joints
Method of sections
External Equilibrium: to find the reaction forces, follow the below steps:
Draw the FBD for the entire truss system.
Determine the reactions. Using the equations of (2 D) which states:

3. Analysis of Trusses Lecture 7
Method of Joints: to find the forces in any member, choose a joint, to which that member is connected, and follow the below steps:
Draw the FBD for the entire truss system.
Determine the reactions. Using the equations of (2 D) which states:
Choose the joint, and draw FBD of a joint with at least one known force and at most two unknown forces.
Using the equation of (2 D) which states:
The internal forces are determined.
Choose another joint.

4. Analysis of Trusses Lecture 7
Method of section (Internal equilibrium): to find the forces in any member, choose a section, to which that member is appeared as an internal force, and follow the below steps:
Draw the FBD for the entire truss system.
Determine the reactions. Using the equations of (2 D) which states:
Choose the section, and draw FBD of that section, shows how the forces replace the sectioned members.
Using the equation of (2 D) which states:
The internal forces are determined.
Choose another section or joint.

5. Analysis of Trusses Analysis of trusses (Zero-force members):
Lecture 7
Analysis of trusses (Zero-force members):
Analysis of trusses system is simplified if one can identify those members that support no loads. We call these zero-force members.
Examples to follow:
If two members form a truss joint and there is no external load or support reaction at that joint then those members are zero-force members.
Joints D and A in the following figure are the joints with no external load or support reaction, so:
FAF = FAB = FDE = FDC = 0.

6. Analysis of Trusses Analysis of trusses (Zero-force members):
Lecture 7
Analysis of trusses (Zero-force members):
Examples to follow:
If three members form a truss joint and there is no external load or support reaction at that joint and two of those members are collinear then the third member is a zero-force member.
In the following figure, AC and AD are zero-force members, because Joints D and A in the following figure are the joints with three members, there is no external load or support reaction, so:
FCA = FDA = 0

7. EXAMPLES of Trusses: Lecture 7
Example 1: Determine the support reactions in the joints of the following truss. Calculate the force in member (BA & BC.)
Solution
1. Draw FBD of entire truss and solve for support reactions:
2. Draw FBD of a joint with at least one known force and at most two unknown forces. We choose joint B.
Assume BC is in compression.

8. EXAMPLES of Trusses: Lecture 7
Example 2: In the following Bowstring Truss, find the force in member (CF).
Solution
draw the FBD and find the support reactions which are shown below
MA = 0
RE * 16 – 5 * 8 – 3 * 12 = 0
RE = 4.75 kN
Fy = 0
RE + RA – 5– 3 = 0
RA = 3.25 kN G C D E O F
4 m
2 m
6 m X

9. EXAMPLES of Trusses: Lecture 7
Example 3: In the following truss, find the force in member (EB).
Solution
Notice that no single cut will provide the answer. Hence, it is best to consider section (a-a and b-b).
MA = 0
RC * 8 – 1000 * 6 – 1000 * 4 – 3000 * 2 = 0
RC = 2000 N
Fy = 0
RA + RC – 1000 – 1000 – = 0
RA = 4000 N
Taking the moment about joint (B), to find (FED), as shown in below figure:
MB = 0
1000 * * 2 – 4000 * FED * sin30o * 4 = 0
FED = 3000 N (compression)

10. Lecture 7
Continue Example 3:
From joint (E) to find (FEB), as shown in below figure:
Fx = 0
FEF . cos30o– 3000 cos30o = 0
FEF = N (compression)
Fy = 0
FEF . Sin30o sin30o FEB = 0
FEF = 2000 N (Tension)