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FE daily problem for October 5, 2026 (Truss member force)

By Dr. Mohamed Elansary, PhD Environmental EngineeringUpdated

This is the FE practice problem that Engineer Exam Lab members worked on October 5, 2026. The topic is truss member force, from the FE Civil exam specification. Try it with the FE Reference Handbook open before you read on. The worked solution below gives the handbook section and page, the equation, every substitution with units, a size check, and the mistake behind each wrong answer.

The problem

Daily problem · FE Civil, Truss member force

A three-member plane truss has joints A (0, 0), B (9.5, 8.0) and C (13.5, 0), with coordinates in m. The members are AB, BC and AC. A is a pin support and C is a roller on a horizontal surface. Joint B carries a downward load of 185 kN and a horizontal load of 20 kN in the +x direction. The force in member AB is most nearly:

  • A 66.7 kN (T)
  • B 221 kN (C)
  • C 66.7 kN (C)
  • D 43.0 kN (C)

Handbook: Statics, Plane Truss: Method of Joints, FE Reference Handbook 10.6

Commit to an answer before you scroll. Writing the given values with their units first is the fastest way to spot what the question really asks for.

Worked solution, step by step

  • Answer: C (66.7 kN in compression)
  • Given: L = 13.5 m, a = 9.5 m, h = 8.0 m, P = 185 kN, H = 20 kN
  • Find: force in member AB, magnitude and tension (T) or compression (C)
  • Handbook: Statics, Plane Truss: Method of Joints, page 98
  • Equation: Method of joints: sum Fx = 0 and sum Fy = 0 at each joint; reactions from sum of moments = 0; tension positive

Substitute, keeping the units on every value:

  1. Reactions, sum of moments about A = 0: Cy = (P·a + H·h)/L = ((185 kN)(9.5 m) + (20 kN)(8.0 m))/(13.5 m) = 142.0 kN
  2. Sum Fy = 0: Ay = P - Cy = 42.96 kN; sum Fx = 0: Ax = -H = -20 kN
  3. Length AB = √(a² + h²) = √(9.5² + 8.0²) m = 12.42 m
  4. Joint A, sum Fy = 0: Ay + F_AB(h/AB) = 0, so F_AB = -Ay·AB/h = -(42.96 kN)(12.42 m)/(8.0 m) = -66.70 kN
  5. F_AB = -66.70 kN, so AB carries 66.7 kN in compression (C)

Result: 66.7 kN (C), 3 significant figures.

Check: With all three member forces, joint B also balances (sum Fx = 0 and sum Fy = 0 including the load); a positive member force is tension, a negative one compression.

Why each wrong option is wrong

Every wrong option on this problem comes from a named mistake, so a wrong pick tells you exactly what to fix:

  • A (66.7 kN (T)): has the right size but the wrong sense; equilibrium of joint A puts AB in compression.
  • B (221 kN (C)): used the reaction at C in the equilibrium of joint A.
  • D (43.0 kN (C)): set the member force equal to the reaction without resolving it along the member.

Where this is in the FE Reference Handbook

This problem uses Statics, Plane Truss: Method of Joints, page 98 of FE Reference Handbook 10.6. The handbook is a free PDF in MyNCEES, and on exam day you search the same document on screen, so practice finding the section with the search box instead of from memory. Search for the name of the quantity you need, not the symbol, and check the page heading before you copy an equation.

How to approach problems like this

Work the number out before you look at the options. The wrong options are built from real mistakes, so a value that matches one of them proves nothing on its own. Write the given values with units, find the equation in the handbook with the search box, and substitute with the units attached. When your result lands on an option, run a quick size check: is the magnitude reasonable for the situation, and do the units reduce to what the question asks for? If your result falls between two options, look for a unit conversion you skipped.

Whatever the result, log it. A short error log with one line per missed problem (the topic, the mistake named in the solution, and the handbook page) shows within a few weeks which habits cost you points, and it turns review time into targeted practice instead of rereading.

For ten more problems on this topic, each with a full solution, see the truss member force practice set. Every past daily problem is in the daily problem archive, one page per day.

Frequently asked questions

Is this a real FE exam question?

No. It is an original problem that our problem engine generated from the formulas in the FE Reference Handbook and checked by code before it was posted. Real exam questions are confidential, and the agreement every examinee accepts forbids sharing them.

Why does this problem appear here a day late?

Members of Engineer Exam Lab get each problem first, in the morning, and the worked solution the same evening. The problem and its solution come to this public archive the next day.

How should I use the worked solution?

Compare your work with it line by line, not only the final answer. If you picked a wrong answer, find the note that matches it above; each one names the exact mistake, which is the habit to fix before exam day.

Sources

  1. NCEES FE Reference Handbook 10.6 (free PDF in MyNCEES). Retrieved October 3, 2026.
  2. NCEES FE Civil CBT exam specifications (PDF). Retrieved October 3, 2026.