A 10 m simply supported beam carries a 40 kN point load 3 m from A and a 12 kN/m uniform load over the full span. Find both reactions.

Start with the thinking

• Replace the distributed load with its resultant at midspan.
• Sum moments about A so R_A drops out of that equation.

Step-by-step solution

1. UDL resultant

   $$W = wL = 12(10) = 120 kN at 5.00 m$$

2. Moments about A — ΣM_A = 0: R_B(10) = 40(3) + 120(5)

3. Right side — 120 + 600 = 720 kN·m

4. Reaction

   $$R_B = 720/10 = 72.0 kN$$

5. Vertical equilibrium

   $$R_A = 40 + 120 - 72.0 = 88.0 kN$$

Why the other options are there

• 80/80 kN (point load position ignored)
• R_A = 72, R_B = 88 (reactions swapped)

Reference: FE Reference Handbook — Statics — Equilibrium of rigid bodies

A statics problem uses Simply supported beam reaction. Given point load (P) = 35.5000 kip; load location (a) = 17.5000 ft; span (L) = 14.0000 ft, determine the far reaction (Rb) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except Rb is given, so isolate Rb 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3 — List the givens: point load (P) = 35.5000 kip, load location (a) = 17.5000 ft, span (L) = 14.0000 ft.

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

5. Step 5 — Evaluate:

   $$Rb = 44.3750\ \text{kip}$$

6. Step 6 — Check: returning Rb = 44.3750 kip to

   $$R_b = P a / L$$

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

Why the other options are there

• 88.7500 — kept a factor of two that cancels in the correct rearrangement.
• 22.1875 — dropped that same factor in the other direction.
• 48.8125 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given load location (a) = 4.0000 ft; span (L) = 16.0000 ft; far reaction (Rb) = 49.7400 kip, determine the point load (P) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3

   $$List the givens: load location (a) = 4.0000 ft, span (L) = 16.0000 ft, far reaction (Rb) = 49.7400 kip$$

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

5. Step 5 — Evaluate:

   $$P = 199.0\ \text{kip}$$

6. Step 6 — Check: returning P = 199.0 kip to

   $$R_b = P a / L$$

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

Why the other options are there

• 397.9 — kept a factor of two that cancels in the correct rearrangement.
• 99.4800 — dropped that same factor in the other direction.
• 218.9 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given point load (P) = 44.5000 kip; span (L) = 34.0000 ft; far reaction (Rb) = 47.9400 kip, determine the load location (a) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except a is given, so isolate a 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3

   $$List the givens: point load (P) = 44.5000 kip, span (L) = 34.0000 ft, far reaction (Rb) = 47.9400 kip$$

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

5. Step 5 — Evaluate:

   $$a = 36.6283\ \text{ft}$$

6. Step 6 — Check: returning a = 36.6283 ft to

   $$R_b = P a / L$$

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

Why the other options are there

• 73.2566 — kept a factor of two that cancels in the correct rearrangement.
• 18.3142 — dropped that same factor in the other direction.
• 40.2911 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given point load (P) = 17.0000 kip; load location (a) = 14.0000 ft; far reaction (Rb) = 48.6700 kip, determine the span (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except L is given, so isolate L 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3 — List the givens: point load (P) = 17.0000 kip, load location (a) = 14.0000 ft, far reaction (Rb) = 48.6700 kip.

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

5. Step 5 — Evaluate:

   $$L = 4.8901\ \text{ft}$$

6. Step 6 — Check: returning L = 4.8901 ft to

   $$R_b = P a / L$$

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

Why the other options are there

• 9.7802 — kept a factor of two that cancels in the correct rearrangement.
• 2.4450 — dropped that same factor in the other direction.
• 5.3791 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given point load (P) = 28.0000 kip; load location (a) = 4.0000 ft; span (L) = 22.0000 ft, determine the far reaction (Rb) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except Rb is given, so isolate Rb 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3 — List the givens: point load (P) = 28.0000 kip, load location (a) = 4.0000 ft, span (L) = 22.0000 ft.

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

5. Step 5 — Evaluate:

   $$Rb = 5.0909\ \text{kip}$$

6. Step 6 — Check: returning Rb = 5.0909 kip to

   $$R_b = P a / L$$

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

Why the other options are there

• 10.1818 — kept a factor of two that cancels in the correct rearrangement.
• 2.5455 — dropped that same factor in the other direction.
• 5.6000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given load location (a) = 5.5000 ft; span (L) = 28.0000 ft; far reaction (Rb) = 9.8000 kip, determine the point load (P) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3

   $$List the givens: load location (a) = 5.5000 ft, span (L) = 28.0000 ft, far reaction (Rb) = 9.8000 kip$$

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

5. Step 5 — Evaluate:

   $$P = 49.8909\ \text{kip}$$

6. Step 6 — Check: returning P = 49.8909 kip to

   $$R_b = P a / L$$

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

Why the other options are there

• 99.7818 — kept a factor of two that cancels in the correct rearrangement.
• 24.9455 — dropped that same factor in the other direction.
• 54.8800 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given point load (P) = 27.5000 kip; span (L) = 33.0000 ft; far reaction (Rb) = 31.6700 kip, determine the load location (a) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except a is given, so isolate a 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3

   $$List the givens: point load (P) = 27.5000 kip, span (L) = 33.0000 ft, far reaction (Rb) = 31.6700 kip$$

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

5. Step 5 — Evaluate:

   $$a = 38.0040\ \text{ft}$$

6. Step 6 — Check: returning a = 38.0040 ft to

   $$R_b = P a / L$$

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

Why the other options are there

• 76.0080 — kept a factor of two that cancels in the correct rearrangement.
• 19.0020 — dropped that same factor in the other direction.
• 41.8044 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given point load (P) = 8.0000 kip; load location (a) = 7.5000 ft; far reaction (Rb) = 31.5200 kip, determine the span (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except L is given, so isolate L 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3 — List the givens: point load (P) = 8.0000 kip, load location (a) = 7.5000 ft, far reaction (Rb) = 31.5200 kip.

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

5. Step 5 — Evaluate:

   $$L = 1.9036\ \text{ft}$$

6. Step 6 — Check: returning L = 1.9036 ft to

   $$R_b = P a / L$$

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

Why the other options are there

• 3.8071 — kept a factor of two that cancels in the correct rearrangement.
• 0.9518 — dropped that same factor in the other direction.
• 2.0939 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements

A statics problem uses Simply supported beam reaction. Given point load (P) = 9.0000 kip; load location (a) = 3.0000 ft; span (L) = 24.0000 ft, determine the far reaction (Rb) in kip.

Start with the thinking

• The governing relation printed in this handbook section is Simply supported beam reaction.
• Everything except Rb is given, so isolate Rb 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.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R_b = P a / L$$

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

3. Step 3 — List the givens: point load (P) = 9.0000 kip, load location (a) = 3.0000 ft, span (L) = 24.0000 ft.

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

5. Step 5 — Evaluate:

   $$Rb = 1.1250\ \text{kip}$$

6. Step 6 — Check: returning Rb = 1.1250 kip to

   $$R_b = P a / L$$

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

Why the other options are there

• 2.2500 — kept a factor of two that cancels in the correct rearrangement.
• 0.5625 — dropped that same factor in the other direction.
• 1.2375 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Equilibrium Requirements