A symmetric pin-jointed truss of span 12 m and height 4 m carries 60 kN at the apex. Find the force in each of the two inclined top members.

Start with the thinking

• Symmetry means each inclined member carries half the vertical load.
• Resolve at the apex joint using the member slope.

Step-by-step solution

1. Member length

   $$L = \sqrt(6^{2} + 4^{2}) = 7.21 m$$

2. Vertical component per member

   $$Fv = 60/2 = 30.0 kN$$

3. Slope ratio

   $$L/height = 7.21/4 = 1.803$$

4. Member force

   $$F = Fv(L/height) = 30.0(1.803)$$

5. Result

   $$F = 54.1 kN compression in each inclined member$$

Why the other options are there

• 30.0 kN (vertical component reported as member force)
• 45.0 kN (horizontal projection used)

Reference: FE Reference Handbook — Statics — Trusses

For a 20 m simple span, what is the influence-line ordinate for R_A when a unit load sits 6 m from B, and what is R_A for a 150 kN axle there?

Start with the thinking

• The influence line for R_A is a straight line from 1.0 at A to 0 at B.
• Ordinate equals the distance from B divided by the span.

Step-by-step solution

1. Ordinate

   $$\eta = (L - x)/L with x measured from A$$

2. Substitute

   $$\eta = (20 - 14)/20 = 0.300$$

3. Reaction

   $$R_A = P\eta = 150(0.300)$$

4. Result

   $$R_A = 45.0 kN$$

5. Check — R_B = 150 − 45.0 = 105 kN, consistent with the load sitting near B ✓

Why the other options are there

• η = 0.700 (measured from the wrong end)
• R_A = 75 kN (symmetric assumption)

Reference: FE Reference Handbook — Structural Analysis — Influence lines

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 16.0000 kip; influence ordinate (eta) = 0.4400, determine the reaction (R) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: moving load (P) = 16.0000 kip, influence ordinate (eta) = 0.4400$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 7.0400\ \text{kip}$$

6. Step 6 — Check: returning R = 7.0400 kip to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 14.0800 — kept a factor of two that cancels in the correct rearrangement.
• 3.5200 — dropped that same factor in the other direction.
• 7.7440 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given influence ordinate (eta) = 0.5100; reaction (R) = 37.8100 kip, determine the moving load (P) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except P is given, so isolate P symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3

   $$List the givens: influence ordinate (eta) = 0.5100, reaction (R) = 37.8100 kip$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 74.1373\ \text{kip}$$

6. Step 6 — Check: returning P = 74.1373 kip to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 148.3 — kept a factor of two that cancels in the correct rearrangement.
• 37.0686 — dropped that same factor in the other direction.
• 81.5510 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 47.0000 kip; reaction (R) = 52.1600 kip, determine the influence ordinate (eta).

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except eta is given, so isolate eta symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that eta stands alone on the left-hand side.

3. Step 3

   $$List the givens: moving load (P) = 47.0000 kip, reaction (R) = 52.1600 kip$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\eta = 1.1098$$

6. Step 6 — Check: returning eta = 1.1098 to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2.2196 — kept a factor of two that cancels in the correct rearrangement.
• 0.5549 — dropped that same factor in the other direction.
• 1.2208 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 60.0000 kip; influence ordinate (eta) = 0.3200, determine the reaction (R) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: moving load (P) = 60.0000 kip, influence ordinate (eta) = 0.3200$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 19.2000\ \text{kip}$$

6. Step 6 — Check: returning R = 19.2000 kip to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 38.4000 — kept a factor of two that cancels in the correct rearrangement.
• 9.6000 — dropped that same factor in the other direction.
• 21.1200 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given influence ordinate (eta) = 0.6400; reaction (R) = 46.3500 kip, determine the moving load (P) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except P is given, so isolate P symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3

   $$List the givens: influence ordinate (eta) = 0.6400, reaction (R) = 46.3500 kip$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 72.4219\ \text{kip}$$

6. Step 6 — Check: returning P = 72.4219 kip to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 144.8 — kept a factor of two that cancels in the correct rearrangement.
• 36.2109 — dropped that same factor in the other direction.
• 79.6641 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 28.0000 kip; reaction (R) = 20.3800 kip, determine the influence ordinate (eta).

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except eta is given, so isolate eta symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that eta stands alone on the left-hand side.

3. Step 3

   $$List the givens: moving load (P) = 28.0000 kip, reaction (R) = 20.3800 kip$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\eta = 0.7279$$

6. Step 6 — Check: returning eta = 0.7279 to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.4557 — kept a factor of two that cancels in the correct rearrangement.
• 0.3639 — dropped that same factor in the other direction.
• 0.8006 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 31.0000 kip; influence ordinate (eta) = 0.5800, determine the reaction (R) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: moving load (P) = 31.0000 kip, influence ordinate (eta) = 0.5800$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 17.9800\ \text{kip}$$

6. Step 6 — Check: returning R = 17.9800 kip to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 35.9600 — kept a factor of two that cancels in the correct rearrangement.
• 8.9900 — dropped that same factor in the other direction.
• 19.7780 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses

A structural analysis problem uses Reaction from influence-line ordinate. Given influence ordinate (eta) = 0.1000; reaction (R) = 4.0600 kip, determine the moving load (P) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Reaction from influence-line ordinate.
• Everything except P is given, so isolate P symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Structural Analysis items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = P \times \eta$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3

   $$List the givens: influence ordinate (eta) = 0.1000, reaction (R) = 4.0600 kip$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 40.6000\ \text{kip}$$

6. Step 6 — Check: returning P = 40.6000 kip to

   $$R = P \times \eta$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 81.2000 — kept a factor of two that cancels in the correct rearrangement.
• 20.3000 — dropped that same factor in the other direction.
• 44.6600 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Influence Lines for Beams and Trusses