The Efficient Engineer Explains Trusses: Joints, Sections, and Load Paths

Overview

The Efficient Engineer explains what a truss is, the pinned-joint assumptions, and why loads are applied only at joints. He shows how a triangle base provides stability, why a four-sided shape is unstable without diagonals, and how diagonal bracing creates triangulated structures. The video then outlines planar trusses analyzed in two dimensions, with examples of common designs and how loads are carried through members in tension or compression.

Key Methods

Two main analysis methods are introduced: the method of joints and the method of sections. The presenter guides viewers through free-body diagrams, equilibrium equations, and trigonometry to determine member forces. Zero force members and symmetry considerations are discussed to simplify solving trusses.

Introduction to Trusses and Basic Stability

The video begins by defining a truss as a rigid assembly of straight members with joints that can be treated as pin connections. With joints pinned, members carry only axial forces, and loads are assumed to act only at joints. The base geometry of a truss is discussed: a triangle is inherently stable since the lengths of the members fix the angles; adding a fourth member (a quadrilateral) without triangulation allows the structure to deform because angles can change while lengths stay fixed. The solution is to triangulate by inserting a diagonal brace, which subdivides the quadrilateral into triangles and yields a stable configuration. This concept underpins many common truss designs.

Planar vs Space Trusses

Most trusses are planar, meaning all members lie in a single plane and can be analyzed in two dimensions. However, some structures behave like space trusses with three-dimensional geometry. The video uses a bridge example to illustrate that loads travel along members within their own plane, validating planar analysis for many real-world bridges where the vertical loads are transmitted to vertical trusses by floor beams in the same plane.

Assumptions and Equilibrium

Two key assumptions are highlighted: joints are pinned, and loads occur only at joints. Because there are no bending moments in members, each end of a member must be in equilibrium with the other end. If a member is in tension, it pulls away from the joint; if in compression, it pushes toward the joint. These conventions set the stage for methodical force calculations using equilibrium equations.

Method of Joints

The method of joints starts with drawing the external-load Free-Body Diagram (FBD) and computing reactions via the three equilibrium equations. Then you analyze each joint, one by one, to solve for unknown member forces. The presenter emphasizes identifying force directions by initially assuming all members are in tension; negative results indicate compression. An emphasis on trigonometry helps resolve forces at joints where members meet at angles, such as a 60-degree angle in the worked example.

Symmetry and Zero-Force Members

Symmetry is used to infer that forces on opposite sides must be identical, speeding up calculations. The video also introduces zero-force members, which carry no load under certain joint configurations. Specifically, a joint with three members where two are colinear and no external load will result in the non-colinear member carrying zero force. A joint with two non-aligned members and no external load must also be zero-force. External loads invalidate these configurations, but without loads these zero-force members help with stability and buckling resistance.

Method of Sections

The method of sections complements the joints approach by “cutting” through the truss to expose a subset of members. After the cut, you solve the internal forces in the cut members using equilibrium in the same way as for joints. The presenter cautions that you should not cut through too many members, since you then have more unknowns than equations. This method is especially useful when you care about a few members in a larger truss.

Worked Examples: Joints and Sections

Two examples are presented: a simple truss solved by joints and a larger truss where the method of sections isolates three members to determine their forces. In the section example, FE is found to be 12 kN, GE is 21 kN, and FD is -30 kN, indicating one compression member and two in tension. The video also discusses how these calculations establish whether a truss is statically determinate or indeterminate, and notes that indeterminate cases require additional methods beyond equilibrium, such as force or displacement methods.

Truss Design Variants and 3D Considerations

The video compares Howe, Pratt, and Warren trusses, noting the typical load paths and where tensions or compressions are concentrated in each design. It explains how verticals and diagonals behave in different configurations and why longer compressive members are less economical due to buckling risk. The final sections introduce space trusses, which, while analyzed similarly to planar trusses, require six equations and a joint with three equations for each node. The takeaway is that 3D trusses are analyzed with the same principles but with greater mathematical complexity.

Conclusion

The Efficient Engineer emphasizes that the strength and efficiency of trusses come from their geometry and the use of pinned joints, allowing axial forces to govern behavior. The video closes with an invitation to subscribe for more on how these structural principles translate into real-world engineering design.