A simply supported beam spans 32 ft under a uniform load of 5.50 kip/ft. Find the maximum shear and moment.

Start with the thinking

• Maximum shear sits at the supports, maximum moment at midspan.
• wL²/8 is worth memorising.

Step-by-step solution

1. Reactions

   $$R = wL/2$$

2. Substituting

   $$R = 5.50(32)/2 = 88.00 kip = V_max$$

3. Midspan moment

   $$M = wL^{2}/8$$

4. Substituting — M = 5.50(32)²/8 = 704.0 kip·ft

Why the other options are there

• 2,816 kip·ft (cantilever formula used)
• 176.0 kip (total load reported as shear)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A 33 ft simple span carries a 25 kip load at midspan. With E = 29,000 ksi and I = 800.0 in⁴, find the midspan deflection.

Start with the thinking

• Deflection scales with L³ — convert to inches before cubing.
• Compare against L/360 for serviceability.

Step-by-step solution

1. Formula

   $$\Delta = PL^{3}/(48EI)$$

2. Span in inches

   $$L = 33 \times 12 = 396 in$$

3. Substituting

   $$\Delta = 25(396)^{3}/(48 \times 29,000 \times 800.0)$$

4. Evaluate

   $$\Delta = 1.3941 in$$

5. Serviceability

   $$L/360 = 1.100 in. \to exceeds the limit$$

Why the other options are there

• 2,409 in. (span left in feet)
• 0.871 in. (uniform-load formula used)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A simply supported beam spans 30 ft under a uniform load of 3.00 kip/ft. Find the maximum shear and moment.

Start with the thinking

• Maximum shear sits at the supports, maximum moment at midspan.
• wL²/8 is worth memorising.

Step-by-step solution

1. Reactions

   $$R = wL/2$$

2. Substituting

   $$R = 3.00(30)/2 = 45.00 kip = V_max$$

3. Midspan moment

   $$M = wL^{2}/8$$

4. Substituting — M = 3.00(30)²/8 = 337.5 kip·ft

Why the other options are there

• 1,350 kip·ft (cantilever formula used)
• 90.00 kip (total load reported as shear)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A 28 ft simple span carries a 11 kip load at midspan. With E = 29,000 ksi and I = 600.0 in⁴, find the midspan deflection.

Start with the thinking

• Deflection scales with L³ — convert to inches before cubing.
• Compare against L/360 for serviceability.

Step-by-step solution

1. Formula

   $$\Delta = PL^{3}/(48EI)$$

2. Span in inches

   $$L = 28 \times 12 = 336 in$$

3. Substituting

   $$\Delta = 11(336)^{3}/(48 \times 29,000 \times 600.0)$$

4. Evaluate

   $$\Delta = 0.4996 in$$

5. Serviceability

   $$L/360 = 0.933 in. \to acceptable$$

Why the other options are there

• 863.3 in. (span left in feet)
• 0.312 in. (uniform-load formula used)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A simply supported beam spans 37 ft under a uniform load of 3.00 kip/ft. Find the maximum shear and moment.

Start with the thinking

• Maximum shear sits at the supports, maximum moment at midspan.
• wL²/8 is worth memorising.

Step-by-step solution

1. Reactions

   $$R = wL/2$$

2. Substituting

   $$R = 3.00(37)/2 = 55.50 kip = V_max$$

3. Midspan moment

   $$M = wL^{2}/8$$

4. Substituting — M = 3.00(37)²/8 = 513.4 kip·ft

Why the other options are there

• 2,054 kip·ft (cantilever formula used)
• 111.0 kip (total load reported as shear)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A 21 ft simple span carries a 25 kip load at midspan. With E = 29,000 ksi and I = 850.0 in⁴, find the midspan deflection.

Start with the thinking

• Deflection scales with L³ — convert to inches before cubing.
• Compare against L/360 for serviceability.

Step-by-step solution

1. Formula

   $$\Delta = PL^{3}/(48EI)$$

2. Span in inches

   $$L = 21 \times 12 = 252 in$$

3. Substituting

   $$\Delta = 25(252)^{3}/(48 \times 29,000 \times 850.0)$$

4. Evaluate

   $$\Delta = 0.3381 in$$

5. Serviceability

   $$L/360 = 0.700 in. \to acceptable$$

Why the other options are there

• 584.3 in. (span left in feet)
• 0.211 in. (uniform-load formula used)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A simply supported beam spans 20 ft under a uniform load of 2.00 kip/ft. Find the maximum shear and moment.

Start with the thinking

• Maximum shear sits at the supports, maximum moment at midspan.
• wL²/8 is worth memorising.

Step-by-step solution

1. Reactions

   $$R = wL/2$$

2. Substituting

   $$R = 2.00(20)/2 = 20.00 kip = V_max$$

3. Midspan moment

   $$M = wL^{2}/8$$

4. Substituting — M = 2.00(20)²/8 = 100.0 kip·ft

Why the other options are there

• 400.0 kip·ft (cantilever formula used)
• 40.00 kip (total load reported as shear)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A 30 ft simple span carries a 8 kip load at midspan. With E = 29,000 ksi and I = 1,550 in⁴, find the midspan deflection.

Start with the thinking

• Deflection scales with L³ — convert to inches before cubing.
• Compare against L/360 for serviceability.

Step-by-step solution

1. Formula

   $$\Delta = PL^{3}/(48EI)$$

2. Span in inches

   $$L = 30 \times 12 = 360 in$$

3. Substituting

   $$\Delta = 8(360)^{3}/(48 \times 29,000 \times 1,550)$$

4. Evaluate

   $$\Delta = 0.1730 in$$

5. Serviceability

   $$L/360 = 1.000 in. \to acceptable$$

Why the other options are there

• 298.9 in. (span left in feet)
• 0.108 in. (uniform-load formula used)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A simply supported beam spans 42 ft under a uniform load of 5.50 kip/ft. Find the maximum shear and moment.

Start with the thinking

• Maximum shear sits at the supports, maximum moment at midspan.
• wL²/8 is worth memorising.

Step-by-step solution

1. Reactions

   $$R = wL/2$$

2. Substituting

   $$R = 5.50(42)/2 = 115.5 kip = V_max$$

3. Midspan moment

   $$M = wL^{2}/8$$

4. Substituting — M = 5.50(42)²/8 = 1,213 kip·ft

Why the other options are there

• 4,851 kip·ft (cantilever formula used)
• 231.0 kip (total load reported as shear)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover

A 25 ft simple span carries a 29 kip load at midspan. With E = 29,000 ksi and I = 400.0 in⁴, find the midspan deflection.

Start with the thinking

• Deflection scales with L³ — convert to inches before cubing.
• Compare against L/360 for serviceability.

Step-by-step solution

1. Formula

   $$\Delta = PL^{3}/(48EI)$$

2. Span in inches

   $$L = 25 \times 12 = 300 in$$

3. Substituting

   $$\Delta = 29(300)^{3}/(48 \times 29,000 \times 400.0)$$

4. Evaluate

   $$\Delta = 1.4063 in$$

5. Serviceability

   $$L/360 = 0.833 in. \to exceeds the limit$$

Why the other options are there

• 2,430 in. (span left in feet)
• 0.879 in. (uniform-load formula used)

Reference: FE Reference Handbook — Structural Analysis → Beam Stiffness and Moment Carryover