1. ES2501: Statics/Unit 16-1: Truss Analysis: the Method of Joints
Truss Structure:
A structure with slender members pin-connected at their
ends, referred as joints, to carry loads at the joints.
To be a truss:
- Nodal loading only;
- All joints pin-connected
Hinged
support
Roller
support
Real physical
Truss
Modeling
Joint/Node
Planar Truss (2D)
Statically determinate Truss
Truss
Truss
Space Truss (3D)
Statically indeterminate Truss

2. ES2501: Statics/Unit 16-2: Truss Analysis: the Method of Joints
Significance of Assumptions in Truss Analysis:
Each member in a truss is a two-force member.
Force of the rest of
the truss on member
AB through a pin at A A A B B
Force of the rest of
the truss on member
AB through a pin at B
Two-force member
in equilibrium A
Two forces must have
the same amplitude,
opposite direction and
along the same line B
- Nodal loading only;
- No moments at node

3. ES2501: Statics/Unit 16-3: Truss Analysis: the Method of Joints
Sign Convention:
In analysis, always starts with the assumed positive direction.
Then, a positive result indicates tension and a negative value
means compression.

4. ES2501: Statics/Unit 16-4: Truss Analysis: the Method of Joints
Method of Joints (Nodal Analysis):
Step 1: Find support reactions;
Step 2: Draw a free-body diagram and list equilibrium
equations for each joint;
Step 3: Select independent equations to solve unknowns.
Example 1:
Reactions:
Free-body diagram of the truss, see the lift figure
Take moment about a point with the most
unknown forces
Equilibrium Equations at Joints:
Equilibrium at C:
Sign
convention
“+” --- tension
“-” --- compression

5. ES2501: Statics/Unit 16-5: Truss Analysis: the Method of Joints
Example 1:
Equilibrium Equations at Joints (con’d):
Equilibrium at C:
Zero-force
member
Equilibrium at A:
Equilibrium at D:
Equilibrium at B:
Zero-force
member
Automatically satisfied

6. ES2501: Statics/Unit 16-6: Truss Analysis: the Method of Joints
Comments:
Method of joints uses equilibrium of joints to list
necessary equations for unknowns;
Method of joints provides complete solution for
internal forces for all members
Identifying zero-force members in a truss may
simplify analysis
Sign convention: Use tension as the conventional
direction for the internal force of any member
“+” --- tension; “-” --- compression
Presentation of results:
Mark the results on the truss
If solving problem manually start with finding the reactions and list
equilibrium equations for nodes with least number of unknowns.

7. ES2501: Statics/Unit 16-7: Truss Analysis: the Method of Joints
Comments (con’d):
Formulate a set of simultaneous linear equations for
a computer solution
Re-collection of equilibrium equations
For truss
For joint C
For joint A:
For joint E
For joint D:
For joint B:
Select independent 10 equations
for 10 unknown:
Computer solution
Note: there for more than 10
equations but only 10 of them
are linearly independent