Consider a light truss, with weight negligible compared with...

Consider a light truss, with weight negligible compared with the load it supports. Suppose it is formed from struts lying in a plane and joined by smooth hinge pins at their ends. External forces act on the truss only at the joints. Figure $\mathrm{P} 12.48$ shows one example of the simplest truss, with three struts and three pins. State reasoning to prove that the force any strut exerts on a pin must be directed along the length of the strut, as a force of tension or compression.

Consider a light truss, with weight negligible compared with the load it supports. Suppose it is formed
from struts lying in a plane and joined by smooth hinge pins at their ends. External forces act on the truss only at the joints. Figure $\mathrm{P} 12.48$ shows one example of the simplest truss, with three struts and three pins. State reasoning to prove that the force any strut exerts on a pin must be directed along the length of the strut, as a force of tension or compression.

Key Concepts

Equilibrium of Forces

The principle of equilibrium of forces states that the sum of all forces acting on a joint must be zero. Since external loads are applied only at the joints, and the joints themselves do not provide moment resistance, the internal forces in the truss members must align with the members. The alignment ensures there are no moment imbalances, thereby satisfying the equilibrium conditions for the entire structure.

Axial Force Transmission

Axial force transmission means that the forces within each truss member are confined to the member’s length, manifesting as either tension or compression. This concept is crucial because any force component perpendicular to a member would generate an unbalanced moment, which cannot occur in an ideal pin-jointed truss under static equilibrium.

Pin-Jointed Connections

Pin-jointed connections, or hinge joints, are assumed to be frictionless and incapable of resisting moments. This means that the forces exerted on and by the joints only have translational effects. Such joints allow the members to pivot freely, which enforces that all forces in the connected members act along the member’s line of action.

Truss Analysis

Truss analysis involves studying structures composed of slender, straight members connected at joints. The key assumption is that the load forces are transmitted solely through the members along their lengths, resulting in pure axial forces. This analysis greatly simplifies the calculation of internal forces in the members, as bending moments and shear forces are neglected.

Transcript

Please give Ace some feedback