A simple span of 55 ft carries a moving load set of 28 kips and 23 kips spaced 8 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 28 + 23 = 51 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 23(8)/51 = 3.608 ft$$

4. Critical offset

   $$e = x̄/2 = 1.804 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (51/55)(27.5 − 1.804)² = 612.3 kip·ft

Why the other options are there

• 701.3 kip·ft (single load at midspan)
• 350.6 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 80 ft carries a moving load set of 11 kips and 16 kips spaced 10 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 11 + 16 = 27 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 16(10)/27 = 5.926 ft$$

4. Critical offset

   $$e = x̄/2 = 2.963 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (27/80)(40 − 2.963)² = 463.0 kip·ft

Why the other options are there

• 540.0 kip·ft (single load at midspan)
• 270.0 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 73 ft carries a moving load set of 14 kips and 21 kips spaced 13 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 14 + 21 = 35 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 21(13)/35 = 7.800 ft$$

4. Critical offset

   $$e = x̄/2 = 3.900 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (35/73)(36.5 − 3.900)² = 509.5 kip·ft

Why the other options are there

• 638.8 kip·ft (single load at midspan)
• 319.4 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 81 ft carries a moving load set of 11 kips and 16 kips spaced 12 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 11 + 16 = 27 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 16(12)/27 = 7.111 ft$$

4. Critical offset

   $$e = x̄/2 = 3.556 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (27/81)(40.5 − 3.556)² = 455.0 kip·ft

Why the other options are there

• 546.8 kip·ft (single load at midspan)
• 273.4 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 62 ft carries a moving load set of 21 kips and 16 kips spaced 16 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 21 + 16 = 37 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 16(16)/37 = 6.919 ft$$

4. Critical offset

   $$e = x̄/2 = 3.459 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (37/62)(31 − 3.459)² = 452.6 kip·ft

Why the other options are there

• 573.5 kip·ft (single load at midspan)
• 286.8 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 40 ft carries a moving load set of 26 kips and 12 kips spaced 8 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 26 + 12 = 38 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 12(8)/38 = 2.526 ft$$

4. Critical offset

   $$e = x̄/2 = 1.263 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (38/40)(20 − 1.263)² = 333.5 kip·ft

Why the other options are there

• 380.0 kip·ft (single load at midspan)
• 190.0 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 54 ft carries a moving load set of 22 kips and 26 kips spaced 7 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 22 + 26 = 48 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 26(7)/48 = 3.792 ft$$

4. Critical offset

   $$e = x̄/2 = 1.896 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (48/54)(27 − 1.896)² = 560.2 kip·ft

Why the other options are there

• 648.0 kip·ft (single load at midspan)
• 324.0 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 88 ft carries a moving load set of 15 kips and 29 kips spaced 9 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 15 + 29 = 44 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 29(9)/44 = 5.932 ft$$

4. Critical offset

   $$e = x̄/2 = 2.966 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (44/88)(44 − 2.966)² = 841.9 kip·ft

Why the other options are there

• 968.0 kip·ft (single load at midspan)
• 484.0 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 41 ft carries a moving load set of 21 kips and 26 kips spaced 9 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 21 + 26 = 47 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 26(9)/47 = 4.979 ft$$

4. Critical offset

   $$e = x̄/2 = 2.489 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (47/41)(20.5 − 2.489)² = 371.9 kip·ft

Why the other options are there

• 481.8 kip·ft (single load at midspan)
• 240.9 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets

A simple span of 49 ft carries a moving load set of 22 kips and 24 kips spaced 7 ft apart. Locate the resultant, then compute the absolute maximum moment under the heavier wheel.

Start with the thinking

• For a moving concentrated load set, the absolute maximum moment occurs when the span centreline bisects the distance between the resultant and the wheel considered.
• Influence-line reasoning locates the critical position before any statics is done.

Step-by-step solution

1. Resultant

   $$R = 22 + 24 = 46 kips$$

2. Formula — x̄ = ΣP d / ΣP (measured from P₁)

3. Substituting

   $$x̄ = 24(7)/46 = 3.652 ft$$

4. Critical offset

   $$e = x̄/2 = 1.826 ft from midspan$$

5. Formula

   $$M_max = (R/L)(L/2 - e)^{2}$$

6. Substituting — M = (46/49)(24.5 − 1.826)² = 482.6 kip·ft

Why the other options are there

• 563.5 kip·ft (single load at midspan)
• 281.8 kip·ft (uniform-load formula)

Reference: FE Reference Handbook — Structural Analysis → Moving Concentrated Load Sets