A statics problem uses Moment of a force. Given force (F) = 544.0 lb; moment arm (d) = 18.7000 ft, determine the moment (M) in lb·ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except M is given, so isolate M 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:

   $$M = F \times d$$

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

3. Step 3

   $$List the givens: force (F) = 544.0 lb, moment arm (d) = 18.7000 ft$$

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

5. Step 5 — Evaluate:

   $$M = 10173\ \text{lb·ft}$$

6. Step 6 — Check: returning M = 10,173 lb·ft to

   $$M = F \times d$$

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

Why the other options are there

• 20,346 — kept a factor of two that cancels in the correct rearrangement.
• 5,086 — dropped that same factor in the other direction.
• 11,190 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moment of Inertia

a cantilevered sign arm Given force (F) = 3,589 N; perpendicular distance (d) = 1.1000 m, determine the moment (M) in N\cdot m.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force about a point.
• Everything except M is given, so isolate M 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.
• A force acting at a perpendicular distance d produces a moment.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for M:

   $$M = M = F d$$

3. Step 3

   $$List the givens: force (F) = 3,589 N, perpendicular distance (d) = 1.1000 m$$

4. Step 4 — Substitute the given values:

   $$M = M = 3589 1.1000$$

5. Step 5 — Evaluate:

   $$M = 3948\ \text{N\cdot m}$$

6. Step 6 — Check: returning M = 3,948 N\cdot m to

   $$M = F d$$

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

Why the other options are there

• 7,895 — kept a factor of two that cancels in the correct rearrangement.
• 1,974 — dropped that same factor in the other direction.
• 4,342 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics (Moments)

A rectangular concrete section's moment of inertia is used in a stiffness calculation. Given width (b) = 5.1000 in; height (h) = 22.7000 in, determine the moment of inertia (I) in in^4.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular moment of inertia.
• Everything except I is given, so isolate I 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.
• The moment of inertia of a rectangular cross section about its centroidal axis governs bending stiffness.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I = \dfrac{b h^3}{12}$$

2. Step 2 — Rearrange symbolically for I:

   $$I = \dfrac{b h^3}{12}$$

3. Step 3

   $$List the givens: width (b) = 5.1000 in, height (h) = 22.7000 in$$

4. Step 4 — Substitute the given values:

   $$I = \dfrac{5.1000 22.7000^3}{12}$$

5. Step 5 — Evaluate:

   I = 4971\ \text{in^4}

6. Step 6 — Check: returning I = 4,971 in^4 to

   $$I = \dfrac{b h^3}{12}$$

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

Why the other options are there

• 9,943 — kept a factor of two that cancels in the correct rearrangement.
• 2,486 — dropped that same factor in the other direction.
• 5,468 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics: Moment of Inertia

A statics problem uses Moment of a force. Given moment arm (d) = 14.5000 ft; moment (M) = 4,488 lb·ft, determine the force (F) in lb.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except F is given, so isolate F 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:

   $$M = F \times d$$

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

3. Step 3 — List the givens: moment arm (d) = 14.5000 ft, moment (M) = 4,488 lb·ft.

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

5. Step 5 — Evaluate:

   $$F = 309.5\ \text{lb}$$

6. Step 6 — Check: returning F = 309.5 lb to

   $$M = F \times d$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Statics → Moment of Inertia

a wrench applied to an anchor nut Given moment (M) = 1,770 N\cdot m; perpendicular distance (d) = 4.0000 m, determine the force (F) in N.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force about a point.
• Everything except F is given, so isolate F 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.
• A force acting at a perpendicular distance d produces a moment.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for F:

   $$F = F = \dfrac{M}{d}$$

3. Step 3

   $$List the givens: moment (M) = 1,770 N\cdot m, perpendicular distance (d) = 4.0000 m$$

4. Step 4 — Substitute the given values:

   $$F = F = \dfrac{1770}{4.0000}$$

5. Step 5 — Evaluate:

   $$F = 442.4\ \text{N}$$

6. Step 6 — Check: returning F = 442.4 N to

   $$M = F d$$

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

Why the other options are there

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

Reference: FE Handbook — Statics (Moments)

A rectangular wood beam's moment of inertia is needed for a deflection check. Given height (h) = 23.2000 in; moment of inertia (I) = 4,695 in^4, determine the width (b) in in.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular moment of inertia.
• Everything except b is given, so isolate b 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.
• The moment of inertia of a rectangular cross section about its centroidal axis governs bending stiffness.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I = \dfrac{b h^3}{12}$$

2. Step 2 — Rearrange symbolically for b:

   $$b = \dfrac{12 I}{h^3}$$

3. Step 3

   $$List the givens: height (h) = 23.2000 in, moment of inertia (I) = 4,695 in^4$$

4. Step 4 — Substitute the given values:

   $$b = \dfrac{12 4695}{23.2000^3}$$

5. Step 5 — Evaluate:

   $$b = 4.5118\ \text{in}$$

6. Step 6 — Check: returning b = 4.5118 in to

   $$I = \dfrac{b h^3}{12}$$

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

Why the other options are there

• 9.0237 — kept a factor of two that cancels in the correct rearrangement.
• 2.2559 — dropped that same factor in the other direction.
• 4.9630 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics: Moment of Inertia

A statics problem uses Moment of a force. Given force (F) = 1,027 lb; moment (M) = 13,314 lb·ft, determine the moment arm (d) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except d is given, so isolate d 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:

   $$M = F \times d$$

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

3. Step 3 — List the givens: force (F) = 1,027 lb, moment (M) = 13,314 lb·ft.

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

5. Step 5 — Evaluate:

   $$d = 12.9640\ \text{ft}$$

6. Step 6 — Check: returning d = 12.9640 ft to

   $$M = F \times d$$

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

Why the other options are there

• 25.9279 — kept a factor of two that cancels in the correct rearrangement.
• 6.4820 — dropped that same factor in the other direction.
• 14.2604 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moment of Inertia

a bracket bolted to a column flange Given moment (M) = 894.5 N\cdot m; force (F) = 3,274 N, determine the perpendicular distance (d) in m.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force about a point.
• Everything except d is given, so isolate d 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.
• A force acting at a perpendicular distance d produces a moment.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for d:

   $$d = d = \dfrac{M}{F}$$

3. Step 3

   $$List the givens: moment (M) = 894.5 N\cdot m, force (F) = 3,274 N$$

4. Step 4 — Substitute the given values:

   $$d = d = \dfrac{894.5}{3274}$$

5. Step 5 — Evaluate:

   $$d = 0.2732\ \text{m}$$

6. Step 6 — Check: returning d = 0.2732 m to

   $$M = F d$$

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

Why the other options are there

• 0.5464 — kept a factor of two that cancels in the correct rearrangement.
• 0.1366 — dropped that same factor in the other direction.
• 0.3005 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics (Moments)

A steel plate's moment of inertia about its centroidal axis is computed for buckling. Given width (b) = 8.4000 in; moment of inertia (I) = 9,676 in^4, determine the height (h) in in.

Start with the thinking

• The governing relation printed in this handbook section is Rectangular moment of inertia.
• Everything except h is given, so isolate h 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.
• The moment of inertia of a rectangular cross section about its centroidal axis governs bending stiffness.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I = \dfrac{b h^3}{12}$$

2. Step 2 — Rearrange symbolically for h:

   $$h = \sqrt[3]{\dfrac{12 I}{b}}$$

3. Step 3

   $$List the givens: width (b) = 8.4000 in, moment of inertia (I) = 9,676 in^4$$

4. Step 4 — Substitute the given values:

   $$h = \sqrt[3]{\dfrac{12 9676}{8.4000}}$$

5. Step 5 — Evaluate:

   $$h = 23.9993\ \text{in}$$

6. Step 6 — Check: returning h = 23.9993 in to

   $$I = \dfrac{b h^3}{12}$$

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

Why the other options are there

• 47.9987 — kept a factor of two that cancels in the correct rearrangement.
• 11.9997 — dropped that same factor in the other direction.
• 26.3993 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics: Moment of Inertia

A statics problem uses Moment of a force. Given force (F) = 76.0000 lb; moment arm (d) = 13.4000 ft, determine the moment (M) in lb·ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except M is given, so isolate M 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:

   $$M = F \times d$$

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

3. Step 3

   $$List the givens: force (F) = 76.0000 lb, moment arm (d) = 13.4000 ft$$

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

5. Step 5 — Evaluate:

   $$M = 1018\ \text{lb·ft}$$

6. Step 6 — Check: returning M = 1,018 lb·ft to

   $$M = F \times d$$

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

Why the other options are there

• 2,037 — kept a factor of two that cancels in the correct rearrangement.
• 509.2 — dropped that same factor in the other direction.
• 1,120 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moment of Inertia