In the analysis of a pin-jointed plane truss, the Method of Joints is based on the premise that
- AThe entire truss is in equilibrium, but individual joints are not.
- BEvery joint in the truss is in equilibrium and the sum of horizontal and vertical forces at each joint must be zero.Correct
- CThe internal members of the truss can resist bending moments and shear forces.
- DThe load is applied directly to the center of the members rather than the joints.
Solution
Concept
Method of Joints in Truss Analysis
Formula
ΣFx = 0, ΣFy = 0
Step-by-step solution
1. Review the given question regarding the fundamental premise of the Method of Joints in truss analysis. 2. Recall that for a pin-jointed 2D truss in static equilibrium, every individual joint must be in equilibrium under concurrent forces, requiring ΣFx = 0 and ΣFy = 0. 3. Compare with the given options and select Option (b) as the correct choice.
Explanation
The Method of Joints works by assuming that if the overall truss is stable, every individual joint inside it must also stay completely still (in equilibrium). Since the joints are connected by smooth pins, no turning forces (moments) exist at the joints, meaning the concurrent forces at any single joint must balance out horizontally and vertically to zero.
Common mistake
A common mistake is selecting Option C by assuming that truss members carry bending moments and shear forces; ideal pin-jointed truss members only carry axial tensile or compressive forces. Another frequent error is selecting Option D by confusing load distribution, whereas ideal truss analysis assumes loads are applied exclusively at the joints.
Correct answer: B) Every joint in the truss is in equilibrium and the sum of horizontal and vertical forces at each joint must be zero.