Questions: Truss Analysis: Joint and Section Methods

Question 1

You need to find the force in a single interior member of a large 20-member truss. Which approach is most efficient?

• A. Method of joints, starting from the nearest support and working inward
• B. Method of sections: cut through the target member and at most two others, then apply equilibrium to one free body
• C. Write the full system of simultaneous equations for all 20 members and solve
• D. Method of joints at every joint sequentially until the interior member is reached

Answer: (B)

The method of sections is designed exactly for this case. By cutting through three members (including the target) and isolating one free body, you get three equilibrium equations (ΣFx, ΣFy, ΣM) for three unknowns — the force in each cut member. With a smart choice of moment center (a point where two of the three cut member forces intersect), one equation isolates the target member's force immediately. The method of joints (options A and D) requires solving every joint from the outside in, which works but is inefficient for finding a single interior member in a large truss.

Question 2

At a pin joint in a truss, two members meet at a right angle and no external load is applied. Based on zero-force member rules, what can be concluded?

• A. Both members carry equal and opposite forces to maintain equilibrium
• B. Both members are zero-force members
• C. The member along the x-axis carries the full load; the member along the y-axis is zero-force
• D. Insufficient information — you must solve the full joint equations to determine this

Answer: (B)

The zero-force member rule states: if only two non-collinear members meet at an unloaded joint, both are zero-force members. With two perpendicular members and no external load, ΣFx = 0 requires the horizontal member to carry zero force, and ΣFy = 0 requires the vertical member to carry zero force. If you set up the equilibrium equations, the only solution is F₁ = F₂ = 0. Identifying zero-force members by inspection (rather than solving equations) is a key efficiency tool that simplifies the analysis of complex trusses.

Question 3

In truss analysis, every member is assumed to carry only axial force (tension or compression) because members are straight, connected by frictionless pins at their ends, and loaded only at joints.

• T. True
• F. False

Answer: True

These three conditions together guarantee that no bending moment can be applied to the ends of a member. A pin transmits forces but not moments. A straight member with forces only at its ends (and no loads along its length) must have those end forces aligned with the member axis — otherwise there would be a net moment on the member. This is the definition of a two-force member. The axial-only assumption reduces each member's unknown from three force components (Fx, Fy, M) to one scalar (magnitude with sign indicating tension or compression), making the problem tractable.

Question 4

In the method of sections, you should typically cut through exactly three members to ensure the resulting equilibrium system is uniquely solvable.

• T. True
• F. False

Answer: False

You need the number of unknown cut member forces to be no greater than the number of available equilibrium equations. In 2D, you have three equations (ΣFx, ΣFy, ΣM). If your cut exposes only two unknown member forces (because the third cut member is already known or is a zero-force member), two equations suffice. Cutting through fewer than three unknowns is valid and sometimes advantageous. The constraint is that you cannot expose more unknowns than equations — cutting through four or more unknown members would give an indeterminate system.

Question 5

Why is the two-force member assumption essential to truss analysis, and how does it simplify the problem compared to analyzing a general rigid frame?

Model answer: The two-force member assumption means each member carries only axial force — tension or compression — with no shear or bending moment at the joints. This reduces each member's unknown from three force components (or a force plus a moment) to a single scalar value. In a general rigid frame (with rigid connections that can transmit moments), each joint equilibrium yields three equations (ΣFx, ΣFy, ΣM) but also introduces moment unknowns at connections, making the system statically indeterminate without further analysis. In a truss with pin joints and loads only at joints, ΣM at any joint is trivially satisfied, leaving only force balance equations — two per joint, one unknown per member. The problem becomes determinate and solvable by working sequentially from joint to joint.

The key simplification is that the pin joint cannot transmit moments, and the two-force member geometry ensures forces are axial. Remove either condition (rigid connections, or distributed loads along members) and you leave truss territory for frame analysis, which is considerably more complex.