A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 20.0000 kip; influence ordinate (eta) = 0.4100, 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

   $$List the givens: moving load (P) = 20.0000 kip, influence ordinate (eta) = 0.4100$$

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

5. Step 5 — Evaluate:

   $$R = 8.2000\ \text{kip}$$

6. Step 6 — Check: returning R = 8.2000 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 16.4000 — kept a factor of two that cancels in the correct rearrangement.
• 4.1000 — dropped that same factor in the other direction.
• 9.0200 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given influence ordinate (eta) = 0.3600; reaction (R) = 59.6700 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

   $$List the givens: influence ordinate (eta) = 0.3600, reaction (R) = 59.6700 kip$$

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

5. Step 5 — Evaluate:

   $$P = 165.8\ \text{kip}$$

6. Step 6 — Check: returning P = 165.8 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 331.5 — kept a factor of two that cancels in the correct rearrangement.
• 82.8750 — dropped that same factor in the other direction.
• 182.3 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 34.0000 kip; reaction (R) = 8.2800 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

   $$List the givens: moving load (P) = 34.0000 kip, reaction (R) = 8.2800 kip$$

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

5. Step 5 — Evaluate:

   $$\eta = 0.2435$$

6. Step 6 — Check: returning eta = 0.2435 to

   $$R = P \times \eta$$

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

Why the other options are there

• 0.4871 — kept a factor of two that cancels in the correct rearrangement.
• 0.1218 — dropped that same factor in the other direction.
• 0.2679 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 31.0000 kip; influence ordinate (eta) = 0.4100, 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

   $$List the givens: moving load (P) = 31.0000 kip, influence ordinate (eta) = 0.4100$$

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

5. Step 5 — Evaluate:

   $$R = 12.7100\ \text{kip}$$

6. Step 6 — Check: returning R = 12.7100 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 25.4200 — kept a factor of two that cancels in the correct rearrangement.
• 6.3550 — dropped that same factor in the other direction.
• 13.9810 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given influence ordinate (eta) = 0.6800; reaction (R) = 52.1400 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

   $$List the givens: influence ordinate (eta) = 0.6800, reaction (R) = 52.1400 kip$$

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

5. Step 5 — Evaluate:

   $$P = 76.6765\ \text{kip}$$

6. Step 6 — Check: returning P = 76.6765 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 153.4 — kept a factor of two that cancels in the correct rearrangement.
• 38.3382 — dropped that same factor in the other direction.
• 84.3441 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 41.0000 kip; reaction (R) = 25.2100 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

   $$List the givens: moving load (P) = 41.0000 kip, reaction (R) = 25.2100 kip$$

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

5. Step 5 — Evaluate:

   $$\eta = 0.6149$$

6. Step 6 — Check: returning eta = 0.6149 to

   $$R = P \times \eta$$

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

Why the other options are there

• 1.2298 — kept a factor of two that cancels in the correct rearrangement.
• 0.3074 — dropped that same factor in the other direction.
• 0.6764 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 46.0000 kip; influence ordinate (eta) = 0.3100, 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

   $$List the givens: moving load (P) = 46.0000 kip, influence ordinate (eta) = 0.3100$$

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

5. Step 5 — Evaluate:

   $$R = 14.2600\ \text{kip}$$

6. Step 6 — Check: returning R = 14.2600 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 28.5200 — kept a factor of two that cancels in the correct rearrangement.
• 7.1300 — dropped that same factor in the other direction.
• 15.6860 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given influence ordinate (eta) = 0.8300; reaction (R) = 30.0300 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

   $$List the givens: influence ordinate (eta) = 0.8300, reaction (R) = 30.0300 kip$$

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

5. Step 5 — Evaluate:

   $$P = 36.1807\ \text{kip}$$

6. Step 6 — Check: returning P = 36.1807 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 72.3614 — kept a factor of two that cancels in the correct rearrangement.
• 18.0904 — dropped that same factor in the other direction.
• 39.7988 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 45.0000 kip; reaction (R) = 51.5600 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

   $$List the givens: moving load (P) = 45.0000 kip, reaction (R) = 51.5600 kip$$

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

5. Step 5 — Evaluate:

   $$\eta = 1.1458$$

6. Step 6 — Check: returning eta = 1.1458 to

   $$R = P \times \eta$$

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

Why the other options are there

• 2.2916 — kept a factor of two that cancels in the correct rearrangement.
• 0.5729 — dropped that same factor in the other direction.
• 1.2604 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures

A structural analysis problem uses Reaction from influence-line ordinate. Given moving load (P) = 35.0000 kip; influence ordinate (eta) = 0.4800, 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

   $$List the givens: moving load (P) = 35.0000 kip, influence ordinate (eta) = 0.4800$$

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

5. Step 5 — Evaluate:

   $$R = 16.8000\ \text{kip}$$

6. Step 6 — Check: returning R = 16.8000 kip to

   $$R = P \times \eta$$

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

Why the other options are there

• 33.6000 — kept a factor of two that cancels in the correct rearrangement.
• 8.4000 — dropped that same factor in the other direction.
• 18.4800 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Structural Analysis → Stability, Determinacy, and Classification of Structures