This guide helps with key concepts for analyzing trusses. Use it as a quick reminder while working on the problems. Examples are included to make things clearer!
Sign Conventions
Signs help us know the direction of forces and moments. Positive (+) and negative (-) depend on the direction.
Forces:
+x: → (to the right)
-x: ← (to the left)
+y: ↑ (upward)
-y: ↓ (downward)
Moments (rotation):
+: ↺ (counterclockwise)
-: ↻ (clockwise)
Example: If a force pushes up (+y), but your calculation gives -50 lb, it means it's actually pushing down.
Order of Operations (PEMDAS)
When doing math in equations, follow this order to avoid mistakes.
Parentheses ( ) first
Exponents & Roots (like ^2 or √)
Multiplication × & Division / (left to right)
Addition + & Subtraction - (left to right)
Example for truss: Moment = 100 lb × (10 ft - 2 ft) = 100 × 8 = 800 lb-ft (do parentheses first!)
Trigonometry Basics
Trig helps break angled forces into horizontal (x) and vertical (y) parts. Use for slanted members.
For a right triangle: a² + b² = c² (Pythagorean theorem)
c = √(a² + b²) to find length.
Vertical part (opposite): a = c × sin(θ)
Horizontal part (adjacent): b = c × cos(θ)
θ is the angle from the horizontal.
To find angle: θ = tan⁻¹(a/b) (also called arctan(a/b))
Example: Member at 30° with force 100 lb.
Horizontal: 100 × cos(30°) ≈ 100 × 0.866 = 86.6 lb
Vertical: 100 × sin(30°) = 100 × 0.5 = 50 lb
Equilibrium Equations
For the structure or joint to be static (not moving), forces and moments must balance to zero.
ΣFx = 0 (all horizontal forces sum to 0)
ΣFy = 0 (all vertical forces sum to 0)
ΣMp = 0 (all moments about point p sum to 0)
Tip: Start with moments (ΣM) about a support to eliminate unknowns. For joints, solve the axis with fewer unknowns first. Horizontal/vertical members only affect one axis (cos=1/sin=0 or vice versa).
Example for joint: ΣFx = FAB × cos(45°) + Rx = 0
Solve for FAB if Rx is known.
Key Vocabulary
Important terms to know for truss analysis.
Joint
Where members connect, like a pin or hinge.
Member
A straight bar or beam connecting two joints.
Truss
A framework of triangles for strength, like in bridges.
Pin Support
Fixed point that resists movement in x and y (2 reactions).
Roller Support
Allows sliding, resists only y movement (1 reaction).
Tension (+)
Force stretching a member, like pulling a rope.
Compression (−)
Force squishing a member, like pushing on a spring.
Reaction
Force from a support pushing back against loads.
Equilibrium
When all forces balance out (nothing moves).
Moment
Twisting effect: force × distance from point.
Method of Joints Tips
- Start at a joint with ≤2 unknowns.
- Assume tension (positive) for unknowns.
- Break angled forces: use sin for y, cos for x.
- Solve one equation, plug into the other.
- Negative result? It's compression—flip the sign for magnitude.
- Move to next joint using solved forces.