Understanding and Analysing Trusses

This paragraph introduces trusses, which are rigid structures made up of straight members used in various applications like bridges, antenna towers, and the International Space Station. It explains the key assumptions for a structure to be considered a truss: pinned connections at joints and loads applied only at the joints. The truss members can only carry axial loads, simplifying the analysis. The base shape of a truss is a triangle, which is stable and doesn't deform under load. Popular truss designs like the Fink roof truss are mentioned, and the distinction between trusses and frames is highlighted. Planar trusses, which can be analyzed as two-dimensional structures, are also discussed. Finally, the paragraph outlines two methods for analyzing trusses: the Method of Joints and the Method of Sections.

The second paragraph delves into the Method of Joints for analyzing trusses. It begins by illustrating how to draw a free body diagram and use equilibrium equations to calculate reaction forces. The process then involves drawing free body diagrams for each joint and solving for unknown forces at the joints. The forces are calculated by considering only the horizontal and vertical components since the joints are pinned, eliminating the need to consider moments. The internal forces in the members are determined by the forces acting on the joints, with tension forces acting away from the joint and compression forces acting towards it. An example is worked through to demonstrate the process, including determining zero force members, which are members that don't carry any load and are often included for stability or safety reasons.

The third paragraph explains the Method of Sections, an alternative approach to analyzing trusses. This method also starts with drawing a free body diagram and calculating reaction forces using equilibrium equations. An imaginary cut is then made through the truss to analyze the internal forces in the members of interest. The internal and external forces on either side of the cut must be in equilibrium, allowing the use of equilibrium equations to solve for the internal forces. The choice of where to make the cut is crucial, as too many unknowns without enough equations can make the problem unsolvable. This method is particularly useful when analyzing a few specific members within a truss with many members. An example demonstrates how to apply the Method of Sections, including handling the assumption of tensile forces and solving for the forces in the members of interest. The concept of a statically determinate truss is introduced, where equilibrium equations can be applied to determine the truss's internal forces.

The final paragraph discusses the historical development of truss designs in the 1840s, specifically the Howe, Pratt, and Warren trusses, which were patented during a period of rapid expansion in the railroad industry. These trusses were typically made from wood and iron. The paragraph explains how understanding the tension and compression forces in truss members can inform about the cost-effectiveness and stability of the design. The Howe truss, with its long and thick diagonal compression members, is less cost-effective. The Pratt truss improves on this by having shorter and thinner diagonal members in tension, which are also less prone to buckling. The Warren truss is noted for its use of equilateral triangles, which simplifies construction and reduces the number of members needed. The forces in the members of these trusses are also observed to change as loads move across a bridge. The paragraph concludes with a brief mention of space trusses, which are three-dimensional and require a different set of equilibrium equations for analysis.