A member of a rigid frame spans 30 ft and carries 2.00 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 2.00(30)²/12 = 150.0 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 2.00(30)²/24 = 75.0 kip·ft

5. Check — simple-span value wL²/8 = 225.0 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 225.0 kip·ft (simple-span value)
• 900.0 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 20 ft and carries 1.25 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 1.25(20)²/12 = 41.7 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 1.25(20)²/24 = 20.8 kip·ft

5. Check — simple-span value wL²/8 = 62.5 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 62.5 kip·ft (simple-span value)
• 250.0 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 19 ft and carries 1.75 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 1.75(19)²/12 = 52.6 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 1.75(19)²/24 = 26.3 kip·ft

5. Check — simple-span value wL²/8 = 79.0 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 79.0 kip·ft (simple-span value)
• 315.9 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 16 ft and carries 1.50 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 1.50(16)²/12 = 32.0 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 1.50(16)²/24 = 16.0 kip·ft

5. Check — simple-span value wL²/8 = 48.0 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 48.0 kip·ft (simple-span value)
• 192.0 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 26 ft and carries 1.50 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 1.50(26)²/12 = 84.5 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 1.50(26)²/24 = 42.3 kip·ft

5. Check — simple-span value wL²/8 = 126.8 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 126.8 kip·ft (simple-span value)
• 507.0 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 26 ft and carries 1.75 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 1.75(26)²/12 = 98.6 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 1.75(26)²/24 = 49.3 kip·ft

5. Check — simple-span value wL²/8 = 147.9 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 147.9 kip·ft (simple-span value)
• 591.5 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 17 ft and carries 3.50 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 3.50(17)²/12 = 84.3 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 3.50(17)²/24 = 42.1 kip·ft

5. Check — simple-span value wL²/8 = 126.4 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 126.4 kip·ft (simple-span value)
• 505.8 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 21 ft and carries 1.25 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 1.25(21)²/12 = 45.9 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 1.25(21)²/24 = 23.0 kip·ft

5. Check — simple-span value wL²/8 = 68.9 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 68.9 kip·ft (simple-span value)
• 275.6 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 22 ft and carries 4.00 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 4.00(22)²/12 = 161.3 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 4.00(22)²/24 = 80.7 kip·ft

5. Check — simple-span value wL²/8 = 242.0 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 242.0 kip·ft (simple-span value)
• 968.0 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame

A member of a rigid frame spans 23 ft and carries 3.75 kip/ft. What are the fixed-end moments, and what is the midspan moment once they are applied?

Start with the thinking

• Fixed-end moment for a uniform load is wL²/12.
• The midspan value is wL²/24 with fixed ends.

Step-by-step solution

1. Fixed-end moment

   $$FEM = wL^{2}/12$$

2. Substituting — FEM = 3.75(23)²/12 = 165.3 kip·ft at each end

3. Midspan

   $$M_mid = wL^{2}/24$$

4. Substituting — M_mid = 3.75(23)²/24 = 82.7 kip·ft

5. Check — simple-span value wL²/8 = 248.0 kip·ft is the sum of the end and mid effects ✓

Why the other options are there

• 248.0 kip·ft (simple-span value)
• 991.9 kip·ft (cantilever value)

Reference: FE Reference Handbook — Structural Analysis → Plane Frame