Source: ENGR 216 Comprehensive Exam Practice Bank | Texas A&M University
Tags: statics, truss, reaction forces, moment, torque, cross product, equilibrium, engineering ethics, fundamental canons, NSPE, ENGR 216
Static equilibrium means the sum of all forces and the sum of all moments about any point are both zero. These two conditions let you solve for unknown support reactions in trusses and brackets. Engineering ethics, governed by canons like the NSPE Code, sets boundaries on what engineers can and cannot sign off on, particularly around competence and scope of practice.
Static equilibrium
A body is in static equilibrium when the net force and the net moment acting on it are both zero. Nothing accelerates; nothing rotates.
Moment (torque)
The rotational effect of a force about a point: M = F × d, where d is the perpendicular distance from the line of action of the force to the point. Positive is typically counterclockwise.
Pin support
A support that prevents translation in both x and y directions but allows rotation. It provides two reaction components: one horizontal, one vertical.
Roller support
A support that prevents translation in one direction only (usually vertical) and allows both rotation and horizontal sliding. It provides one reaction component.
Free body diagram (FBD)
A sketch showing the body isolated from its surroundings, with all external forces and moments drawn in. The essential first step in any statics problem.
NSPE Code of Ethics / Fundamental Canons
The core ethical rules for professional engineers. Six canons covering public safety, competence, honesty, service, conduct, and professional development.
The standard approach for a statically determinate truss:
Draw the free body diagram of the entire truss, replacing supports with their reaction force components.
A pin gives two unknowns (horizontal and vertical). A roller gives one unknown (perpendicular to the rolling surface).
Apply equilibrium: ΣFx = 0, ΣFy = 0, and ΣM about a convenient point = 0.
Choosing the moment point at one support eliminates that support's forces from the moment equation, making the algebra simpler.
Worked approach: truss with 3 kN and 5 kN loads
Without specific geometry given in the problem, the general method is:
Sum moments about pin A to find the vertical reaction at roller D.
Sum moments about D to find the vertical reaction at A.
Sum Fy = 0 as a check: the two vertical reactions should equal the total downward load (3 + 5 = 8 kN).
Sum Fx = 0 to find the horizontal reaction at A (which is zero if all applied loads are vertical).
When a force is applied at an angle, decompose it into horizontal and vertical components before calculating moments.
Worked example: 300 lb force at 22° on a bracket
The force is applied at a point 9 inches vertically and 8 inches horizontally from Point A, at an angle of 22° from some reference.
Decompose the force:
F_x = 300 · cos(22°) ≈ 300 × 0.9272 ≈ 278.2 lb
F_y = 300 · sin(22°) ≈ 300 × 0.3746 ≈ 112.4 lb
Each component produces a moment about A. The moment arm is the perpendicular distance:
The horizontal component (F_x) acts at a vertical distance of 9 in from A: M₁ = 278.2 × 9 = 2503.4 lb·in
The vertical component (F_y) acts at a horizontal distance of 8 in from A: M₂ = 112.4 × 8 = 899.2 lb·in
The total moment depends on the directions (clockwise vs counterclockwise). Assign a sign convention and sum:
If both produce moments in the same rotational sense, add them. If opposite, subtract. Without the full figure, determine the sense from the geometry of the problem.
The NSPE Fundamental Canons most relevant to the exam practice problem:
Canon 1: Hold paramount the safety, health, and welfare of the public
Engineers must prioritise public safety above all other considerations, including employer pressure or commercial interest.
Canon 2: Perform services only in areas of their competence
An engineer must not approve, sign, or seal work outside their area of training and expertise. Signing off on a design you did not supervise and that falls outside your specialty violates this canon directly.
Canon 6: Conduct themselves honourably, responsibly, ethically, and lawfully
Broad professional conduct expectations that reinforce the other canons.
You are asked by your employer to sign off on a design you did not personally supervise and which falls outside your area of expertise.
Two canons are violated:
Canon 2 (competence): you lack the specific expertise to evaluate the design.
Canon 1 (public safety): approving work you cannot properly assess puts the public at risk.
Some formulations may also cite Canon 6 (honourable conduct), but the two most directly relevant are Canons 1 and 2.
Equilibrium conditions: ΣFx = 0, ΣFy = 0, ΣM = 0
Moment of a force: M = F · d (where d is the perpendicular distance to the pivot point)
Force decomposition: F_x = F · cos(θ), F_y = F · sin(θ)
⚠️ Always draw the FBD first. Skipping it is the most common source of errors in statics problems.
⚠️ When summing moments, choose the point strategically. Summing about a pin support eliminates two unknowns from that equation.
⚠️ Sign conventions matter. Pick one (e.g. counterclockwise positive) and stick with it throughout the problem.
⚠️ For the moment problem with an angled force, decompose into components first. Do not try to find a single perpendicular distance to the full force vector unless you are very comfortable with the geometry.
⚠️ The ethics question is straightforward but easy to overthink. The answer is Canon 1 (public safety) and Canon 2 (competence). Know these by number and name.
Q: A horizontal beam is pinned at A and supported by a roller at B, 6 m away. A 10 kN downward load acts 2 m from A. What is the vertical reaction at B?
A: Sum moments about A: R_B × 6 = 10 × 2, so R_B = 20/6 ≈ 3.33 kN upward. Then R_A = 10 − 3.33 = 6.67 kN upward.
Q: Why do we decompose an angled force into components before computing moments?
A: Because the moment of a force depends on the perpendicular distance from the line of action to the pivot point. Decomposing into horizontal and vertical components makes identifying those perpendicular distances straightforward from the given geometry.
Q: An engineer discovers a safety concern in a project but is told by management to ignore it. Which canon applies?
A: Canon 1: hold paramount the safety, health, and welfare of the public. The engineer has an obligation to raise the concern regardless of management pressure.
Q: Can an engineer sign off on a design they supervised if it is outside their field of expertise?
A: No. Canon 2 requires that engineers perform services only in areas of their competence. Supervision alone does not confer the necessary expertise.
statics, static equilibrium, free body diagram, FBD, reaction forces, pin support, roller support, truss analysis, moment, torque, perpendicular distance, force decomposition, component method, NSPE, fundamental canons, engineering ethics, competence, public safety, Canon 1, Canon 2, professional responsibility, ENGR 216, Texas A&M