A floor system carries D = 85 psf, L = 43 psf and Lr = 19 psf. Evaluate the basic strength combinations and identify the governing factored load.

Start with the thinking

• Evaluate every applicable combination — the largest result governs.
• Companion live load enters at 0.5L or 1.0L depending on the combination.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(85) = 119.0 psf$$

2. Combination 2

   $$1.2D + 1.6L + 0.5Lr = 1.2(85) + 1.6(43) + 0.5(19) = 180.3 psf$$

3. Combination 3

   $$1.2D + 1.6Lr + 1.0L = 1.2(85) + 1.6(19) + 1.0(43) = 175.4 psf$$

4. Compare — governing value is 180.3 psf from 1.2D + 1.6L + 0.5Lr

Why the other options are there

• 147.0 psf (service loads added without factors)
• 119.0 psf (only 1.4D evaluated)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A roof beam supports D = 32 psf, L = 95 psf and snow S = 27 psf. Evaluate the ASD combinations and find the governing service load.

Start with the thinking

• ASD combinations use unfactored loads with companion factors of 0.75.
• Do not mix ASD demands with LRFD (φ) capacities.

Step-by-step solution

1. Combination 1

   $$D = 32.0 psf$$

2. Combination 2

   $$D + L = 32 + 95 = 127.0 psf$$

3. Combination 3

   $$D + 0.75L + 0.75S = 32 + 0.75(95) + 0.75(27) = 123.5 psf$$

4. Governing — 127.0 psf from D + L

Why the other options are there

• 190.4 psf (LRFD factors applied in an ASD check)
• 154.0 psf (0.75 companion factors omitted)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A floor beam carries dead load 1.30 kip/ft and live load 1.30 kip/ft. Determine the governing factored load.

Start with the thinking

• Check 1.4D and 1.2D + 1.6L; the larger governs.
• Service loads are never used for strength design.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(1.30) = 1.820 kip/ft$$

2. Combination 2

   $$1.2D + 1.6L = 1.2(1.30) + 1.6(1.30) = 3.640 kip/ft$$

3. Governing

   $$w_u = \max = 3.640 kip/ft$$

Why the other options are there

• 2.60 kip/ft (service load used)
• 1.82 kip/ft (only the dead-load case checked)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A floor beam carries D = 2.1, L = 2.2, L_r = 0.8 and W = 1.0 kip/ft. Evaluate the governing LRFD load combination and, with a resistance factor φ = 0.90, determine the nominal strength the member must provide.

Start with the thinking

• Every ASCE 7-16 combination must be evaluated; the largest result governs the limit state.
• LRFD requires φRn ≥ Ru, so the nominal demand is the factored load divided by φ.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(2.1) = 2.940 kip/ft$$

2. Combination 2

   $$1.2D + 1.6L + 0.5L_r = 6.440 kip/ft$$

3. Combination 3

   $$1.2D + 1.0W + 1.0L + 0.5L_r = 6.120 kip/ft$$

4. Governing

   $$w_u = 6.440 kip/ft$$

5. Formula — φR_n ≥ R_u → R_n ≥ R_u/φ

6. Substituting

   $$R_n = 6.440/0.90 = 7.156 kip/ft$$

Why the other options are there

• 5.10 kip/ft (service loads, unfactored)
• 5.80 kip/ft (multiplied by φ instead of dividing)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A floor system carries D = 76 psf, L = 95 psf and Lr = 20 psf. Evaluate the basic strength combinations and identify the governing factored load.

Start with the thinking

• Evaluate every applicable combination — the largest result governs.
• Companion live load enters at 0.5L or 1.0L depending on the combination.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(76) = 106.4 psf$$

2. Combination 2

   $$1.2D + 1.6L + 0.5Lr = 1.2(76) + 1.6(95) + 0.5(20) = 253.2 psf$$

3. Combination 3

   $$1.2D + 1.6Lr + 1.0L = 1.2(76) + 1.6(20) + 1.0(95) = 218.2 psf$$

4. Compare — governing value is 253.2 psf from 1.2D + 1.6L + 0.5Lr

Why the other options are there

• 191.0 psf (service loads added without factors)
• 106.4 psf (only 1.4D evaluated)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A roof beam supports D = 81 psf, L = 84 psf and snow S = 18 psf. Evaluate the ASD combinations and find the governing service load.

Start with the thinking

• ASD combinations use unfactored loads with companion factors of 0.75.
• Do not mix ASD demands with LRFD (φ) capacities.

Step-by-step solution

1. Combination 1

   $$D = 81.0 psf$$

2. Combination 2

   $$D + L = 81 + 84 = 165.0 psf$$

3. Combination 3

   $$D + 0.75L + 0.75S = 81 + 0.75(84) + 0.75(18) = 157.5 psf$$

4. Governing — 165.0 psf from D + L

Why the other options are there

• 231.6 psf (LRFD factors applied in an ASD check)
• 183.0 psf (0.75 companion factors omitted)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A floor beam carries dead load 0.60 kip/ft and live load 2.10 kip/ft. Determine the governing factored load.

Start with the thinking

• Check 1.4D and 1.2D + 1.6L; the larger governs.
• Service loads are never used for strength design.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(0.60) = 0.840 kip/ft$$

2. Combination 2

   $$1.2D + 1.6L = 1.2(0.60) + 1.6(2.10) = 4.080 kip/ft$$

3. Governing

   $$w_u = \max = 4.080 kip/ft$$

Why the other options are there

• 2.70 kip/ft (service load used)
• 0.84 kip/ft (only the dead-load case checked)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A floor beam carries D = 2.2, L = 1.6, L_r = 0.5 and W = 0.3 kip/ft. Evaluate the governing LRFD load combination and, with a resistance factor φ = 0.90, determine the nominal strength the member must provide.

Start with the thinking

• Every ASCE 7-16 combination must be evaluated; the largest result governs the limit state.
• LRFD requires φRn ≥ Ru, so the nominal demand is the factored load divided by φ.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(2.2) = 3.080 kip/ft$$

2. Combination 2

   $$1.2D + 1.6L + 0.5L_r = 5.450 kip/ft$$

3. Combination 3

   $$1.2D + 1.0W + 1.0L + 0.5L_r = 4.790 kip/ft$$

4. Governing

   $$w_u = 5.450 kip/ft$$

5. Formula — φR_n ≥ R_u → R_n ≥ R_u/φ

6. Substituting

   $$R_n = 5.450/0.90 = 6.056 kip/ft$$

Why the other options are there

• 4.30 kip/ft (service loads, unfactored)
• 4.91 kip/ft (multiplied by φ instead of dividing)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A floor system carries D = 79 psf, L = 76 psf and Lr = 15 psf. Evaluate the basic strength combinations and identify the governing factored load.

Start with the thinking

• Evaluate every applicable combination — the largest result governs.
• Companion live load enters at 0.5L or 1.0L depending on the combination.

Step-by-step solution

1. Combination 1

   $$1.4D = 1.4(79) = 110.6 psf$$

2. Combination 2

   $$1.2D + 1.6L + 0.5Lr = 1.2(79) + 1.6(76) + 0.5(15) = 223.9 psf$$

3. Combination 3

   $$1.2D + 1.6Lr + 1.0L = 1.2(79) + 1.6(15) + 1.0(76) = 194.8 psf$$

4. Compare — governing value is 223.9 psf from 1.2D + 1.6L + 0.5Lr

Why the other options are there

• 170.0 psf (service loads added without factors)
• 110.6 psf (only 1.4D evaluated)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)

A roof beam supports D = 89 psf, L = 45 psf and snow S = 16 psf. Evaluate the ASD combinations and find the governing service load.

Start with the thinking

• ASD combinations use unfactored loads with companion factors of 0.75.
• Do not mix ASD demands with LRFD (φ) capacities.

Step-by-step solution

1. Combination 1

   $$D = 89.0 psf$$

2. Combination 2

   $$D + L = 89 + 45 = 134.0 psf$$

3. Combination 3

   $$D + 0.75L + 0.75S = 89 + 0.75(45) + 0.75(16) = 134.8 psf$$

4. Governing — 134.8 psf from D + 0.75L + 0.75S

Why the other options are there

• 178.8 psf (LRFD factors applied in an ASD check)
• 150.0 psf (0.75 companion factors omitted)

Reference: FE Reference Handbook — Structural Design → Load Combinations using Allowable Stress Design (ASD)