A symmetric plane truss spans 39 ft in 4 equal panels with a depth of 8 ft and has 9 members and 6 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 19 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$9 + 3 = 12 versus 2j = 12 \to determinate$$

3. Reaction

   $$R = P/2 = 19/2 = 9.5 kips$$

4. Panel length

   $$s = 39/4 = 9.75 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 9.5(9.75)/8 = 11.58 kips (tension)$$

Why the other options are there

• 92.6 kips (never divided by the depth)
• 19.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 27 ft in 4 equal panels with a depth of 14 ft and has 9 members and 6 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 21 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$9 + 3 = 12 versus 2j = 12 \to determinate$$

3. Reaction

   $$R = P/2 = 21/2 = 10.5 kips$$

4. Panel length

   $$s = 27/4 = 6.75 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 10.5(6.75)/14 = 5.06 kips (tension)$$

Why the other options are there

• 70.9 kips (never divided by the depth)
• 21.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 58 ft in 8 equal panels with a depth of 10 ft and has 11 members and 7 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 33 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$11 + 3 = 14 versus 2j = 14 \to determinate$$

3. Reaction

   $$R = P/2 = 33/2 = 16.5 kips$$

4. Panel length

   $$s = 58/8 = 7.25 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 16.5(7.25)/10 = 11.96 kips (tension)$$

Why the other options are there

• 119.6 kips (never divided by the depth)
• 33.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 47 ft in 6 equal panels with a depth of 15 ft and has 21 members and 12 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 37 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$21 + 3 = 24 versus 2j = 24 \to determinate$$

3. Reaction

   $$R = P/2 = 37/2 = 18.5 kips$$

4. Panel length

   $$s = 47/6 = 7.83 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 18.5(7.83)/15 = 9.66 kips (tension)$$

Why the other options are there

• 144.9 kips (never divided by the depth)
• 37.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 29 ft in 8 equal panels with a depth of 12 ft and has 17 members and 10 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 31 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$17 + 3 = 20 versus 2j = 20 \to determinate$$

3. Reaction

   $$R = P/2 = 31/2 = 15.5 kips$$

4. Panel length

   $$s = 29/8 = 3.63 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 15.5(3.63)/12 = 4.68 kips (tension)$$

Why the other options are there

• 56.2 kips (never divided by the depth)
• 31.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 27 ft in 4 equal panels with a depth of 15 ft and has 9 members and 6 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 15 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$9 + 3 = 12 versus 2j = 12 \to determinate$$

3. Reaction

   $$R = P/2 = 15/2 = 7.5 kips$$

4. Panel length

   $$s = 27/4 = 6.75 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 7.5(6.75)/15 = 3.38 kips (tension)$$

Why the other options are there

• 50.6 kips (never divided by the depth)
• 15.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 45 ft in 4 equal panels with a depth of 15 ft and has 9 members and 6 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 15 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$9 + 3 = 12 versus 2j = 12 \to determinate$$

3. Reaction

   $$R = P/2 = 15/2 = 7.5 kips$$

4. Panel length

   $$s = 45/4 = 11.25 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 7.5(11.25)/15 = 5.63 kips (tension)$$

Why the other options are there

• 84.4 kips (never divided by the depth)
• 15.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 53 ft in 8 equal panels with a depth of 11 ft and has 21 members and 12 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 25 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$21 + 3 = 24 versus 2j = 24 \to determinate$$

3. Reaction

   $$R = P/2 = 25/2 = 12.5 kips$$

4. Panel length

   $$s = 53/8 = 6.63 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 12.5(6.63)/11 = 7.53 kips (tension)$$

Why the other options are there

• 82.8 kips (never divided by the depth)
• 25.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 52 ft in 8 equal panels with a depth of 8 ft and has 17 members and 10 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 29 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$17 + 3 = 20 versus 2j = 20 \to determinate$$

3. Reaction

   $$R = P/2 = 29/2 = 14.5 kips$$

4. Panel length

   $$s = 52/8 = 6.50 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 14.5(6.50)/8 = 11.78 kips (tension)$$

Why the other options are there

• 94.3 kips (never divided by the depth)
• 29.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss

A symmetric plane truss spans 40 ft in 8 equal panels with a depth of 8 ft and has 11 members and 7 joints. Check static determinacy, then find the bottom-chord force in the first panel for a single 30 kip load at midspan.

Start with the thinking

• A plane truss is statically determinate when m + 3 = 2j.
• One cut through the panel plus moment about the opposite joint gives the chord force directly.

Step-by-step solution

1. Formula

   $$determinacy: m + r = 2j with r = 3$$

2. Substituting

   $$11 + 3 = 14 versus 2j = 14 \to determinate$$

3. Reaction

   $$R = P/2 = 30/2 = 15.0 kips$$

4. Panel length

   $$s = 40/8 = 5.00 ft$$

5. Formula — ΣM at the top joint: F_chord × h = R × s

6. Substituting

   $$F = 15.0(5.00)/8 = 9.38 kips (tension)$$

Why the other options are there

• 75.0 kips (never divided by the depth)
• 30.0 kips (used the whole load)

Reference: FE Reference Handbook — Structural Analysis → Plane Truss