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Exam Answer TemplatesCELE · Structural Theory & Analysis

CELE Structural Theory & Analysis — Loads and Load Combinations (NSCP)Exam Answer Templates

Step-by-step answer templates for Loads and Load Combinations (NSCP), from the Structural Theory & Analysis part of Super Tutor's CELE review.

Loads and Load Combinations (NSCP) - Exam Answer Templates

Knowing the correct answer is only half the battle in the PRC Civil Engineer Licensure Examination. The other half is writing that answer in the precise format, using the exact technical language, and demonstrating the logical step-by-step structure that earns full marks. Examiners follow strict marking schemes: a missing unit, a skipped formula citation, or an incomplete load combination can cost you 1–2 marks per item. These templates show you exactly how a perfect exam answer looks — the phrasing, the structure, the numerical setup, and the conclusion — so you can reproduce it under time pressure. Study each model answer until you can replicate it from memory. The difference between passing and failing the board exam often comes down to disciplined answer writing, not just technical knowledge.

Answer templates

Define dead load as used in structural design under NSCP 2015.

Load Types — Dead Loadeasyvery short answer1 mark

Examiner tip

One clear, complete sentence that includes 'permanent' and lists concrete examples is sufficient. Do not over-explain; VSA answers must be concise.

Model answer

Dead load (D) is the permanent gravity load due to the self-weight of the structural members, architectural finishes, fixed mechanical/electrical equipment, and all other permanently attached components of a building, as defined under NSCP 2015 Section 204.

Answer structure

  • Single sentence: define dead load by naming its sources (self-weight, finishes, fixed equipment) and its permanent nature [1 mark]

Scoring breakdown

1 mark

Criteria

Correct definition that includes the key qualifier 'permanent' AND at least two correct sources (structural self-weight, finishes, fixed equipment)

Common mark deductions

  • Defining dead load as only 'weight of the structure' without mentioning finishes or fixed equipment — too narrow for full credit
  • Calling dead load 'variable' or 'changing' — factually wrong, no mark awarded
  • Omitting the concept of permanence

Key phrases to include

  • permanent
  • self-weight
  • fixed equipment
  • architectural finishes
  • NSCP 2015

State the NSCP 2015 LRFD load combination that governs for most gravity-only loading scenarios (dead load D and live load L only).

NSCP LRFD Load Combinationseasyvery short answer1 mark

Examiner tip

Memorise all seven LRFD combinations verbatim. For a 1-mark VSA the equation alone (with correct factors) is the full answer.

Model answer

The governing LRFD combination for gravity (D and L) is:
U = 1.2D + 1.6L
(NSCP 2015 Section 203.3, Combination 2, with no roof live load or wind/seismic components present.)

Answer structure

  • State the combination equation exactly [1 mark]

Scoring breakdown

1 mark

Criteria

Exact factors: 1.2 on D and 1.6 on L written correctly; partial credit is not given if factors are reversed or incorrect

Common mark deductions

  • Writing 1.4D + 1.7L — old ACI/UBC factors, not current NSCP 2015 LRFD
  • Writing 1.2D + 1.6L + 0.5Lr without being asked about roof load — adds unnecessary terms
  • Confusing this with the ASD combination D + L

Key phrases to include

  • 1.2D
  • 1.6L
  • LRFD
  • NSCP 2015
  • governs

What is the purpose of the 0.9D factor in NSCP 2015 LRFD combination U = 0.9D + 1.0W?

NSCP LRFD Load Combinations — Uplift/Overturningmediumvery short answer1 mark

Examiner tip

The key insight examiners look for is the word 'uplift' or 'overturning' — it shows you understand the physical scenario this combination addresses.

Model answer

The 0.9D factor reduces the stabilising effect of dead load to its minimum probable value, thereby producing the worst-case net uplift or overturning effect when wind load W acts upward or laterally against the structure. It ensures that dead load is not over-credited as a restoring force.

Answer structure

  • State the purpose: worst-case uplift/overturning check by reducing stabilising dead load [1 mark]

Scoring breakdown

1 mark

Criteria

Must convey the concept that 0.9D represents a reduced dead load used to check net uplift or overturning (not the maximum load scenario)

Common mark deductions

  • Saying '0.9D is a safety factor on dead load' without explaining why it is less than 1.0 — incomplete reasoning
  • Confusing this with a load reduction factor for live load

Key phrases to include

  • uplift
  • overturning
  • stabilising effect
  • minimum dead load
  • worst-case

Differentiate between LRFD and ASD design philosophies as applied to load combinations in NSCP 2015. (2 marks)

Design Philosophies — LRFD vs ASDeasyshort answer2 marks

Examiner tip

Use a side-by-side structure: LRFD paragraph, then ASD paragraph. End with the key distinction sentence to show deeper understanding and secure both marks.

Model answer

LRFD (Load and Resistance Factor Design): Loads are multiplied by load factors greater than 1.0 to obtain factored (ultimate) loads (e.g., U = 1.2D + 1.6L). The structure's nominal resistance is then multiplied by a strength-reduction factor φ (< 1.0). Design is acceptable when factored demand ≤ φ × nominal strength.

ASD (Allowable Stress Design): Loads are used at service (unfactored) levels (e.g., D + L). The allowable capacity is the nominal strength divided by a factor of safety (FS). Design is acceptable when service demand ≤ nominal strength / FS.

Key distinction: LRFD amplifies loads and reduces resistance separately for each load type, providing more uniform reliability; ASD uses a single FS and is simpler but less precise in reliability.

Answer structure

  • Point 1: Define LRFD — factored loads, φ-factor on resistance [1 mark]
  • Point 2: Define ASD — service loads, FS on nominal strength [1 mark]

Scoring breakdown

1 mark

Criteria

Correct description of LRFD: load factors > 1.0 applied to loads, φ-factor < 1.0 applied to resistance, checked at ultimate/factored level

1 mark

Criteria

Correct description of ASD: unfactored service loads, nominal strength divided by FS

Common mark deductions

  • Stating LRFD uses a 'factor of safety' — wrong terminology; LRFD uses φ-factors and load factors
  • Failing to mention that ASD uses service (unfactored) loads — this is the defining distinction
  • Giving only one definition without comparing the two approaches

Key phrases to include

  • load factors
  • factored loads
  • strength-reduction factor φ
  • service loads
  • factor of safety
  • nominal strength
  • ultimate

A one-way slab system has beams spaced 3.5 m on centre. The area dead load is 4.8 kPa and the area live load is 2.4 kPa. Determine the service (ASD) line loads on an interior beam. (2 marks)

Tributary Area — Beam Line Loadseasynumerical2 marks

Examiner tip

Always write the formula w = q·s explicitly before substituting. Show wD and wL as separate lines before combining — this earns partial credit even with arithmetic errors.

Model answer

Given:
Beam spacing, s = 3.5 m (interior beam → tributary width = 3.5 m)
Dead load intensity, qD = 4.8 kPa
Live load intensity, qL = 2.4 kPa

Tributary line load formula: w = q × s

Dead load line load:
wD = qD × s = 4.8 × 3.5 = 16.8 kN/m

Live load line load:
wL = qL × s = 2.4 × 3.5 = 8.4 kN/m

ASD service load combination (NSCP 2015 ASD Combo 2: D + L):
w_service = wD + wL = 16.8 + 8.4 = 25.2 kN/m

∴ Service (ASD) line load on interior beam = 25.2 kN/m

Answer structure

  • Step 1: List given data and identify tributary width = beam spacing for interior beam [0.5 mark]
  • Step 2: Apply w = q × s to compute wD and wL separately, with units [1 mark]
  • Step 3: State ASD combination D + L and compute total service load [0.5 mark]

Scoring breakdown

1 mark

Criteria

Correct tributary line loads: wD = 16.8 kN/m AND wL = 8.4 kN/m, with formula shown

1 mark

Criteria

Correct total service load = 25.2 kN/m using ASD Combo 2 (D + L), with units stated

Common mark deductions

  • Using half the spacing for an interior beam — interior beams carry full spacing as tributary width
  • Forgetting to multiply by the spacing and just stating qD = 4.8 kN/m (area load ≠ line load)
  • Omitting units (kN/m) on the final answer

Key phrases to include

  • tributary width
  • w = q × s
  • ASD combination D + L
  • kN/m
  • interior beam

For a simply supported beam with a span of 6 m, dead load wD = 12 kN/m, and live load wL = 6 kN/m, determine the LRFD factored uniform load wu and the factored midspan moment Mu. (2 marks)

LRFD Load Combinations — Beam Designeasynumerical2 marks

Examiner tip

Check: does Combo 1 (1.4D = 1.4×12 = 16.8 kN/m) govern over Combo 2 (24.0 kN/m)? No — always show this comparison to demonstrate rigor.

Model answer

Given:
Span, L = 6 m; wD = 12 kN/m; wL = 6 kN/m

Governing LRFD gravity combination (NSCP 2015 Section 203.3, Combo 2):
wu = 1.2wD + 1.6wL
= 1.2(12) + 1.6(6)
= 14.4 + 9.6
= 24.0 kN/m

Factored midspan moment (simply supported, UDL):
Mu = wuL²/8
= 24.0 × (6)² / 8
= 24.0 × 36 / 8
= 108 kN·m

∴ wu = 24.0 kN/m and Mu = 108 kN·m

Answer structure

  • Step 1: Write LRFD Combo 2 formula and substitute values to get wu [1 mark]
  • Step 2: Apply Mu = wuL²/8 and compute Mu with correct units [1 mark]

Scoring breakdown

1 mark

Criteria

wu = 24.0 kN/m correctly computed using 1.2D + 1.6L with factors shown

1 mark

Criteria

Mu = 108 kN·m correctly computed using wuL²/8, with units kN·m

Common mark deductions

  • Using 1.4D instead of 1.2D for gravity with live load present — Combo 1 (1.4D) is only valid when there is no live load
  • Forgetting to square L in the moment formula — computing wuL/8 instead of wuL²/8
  • Reporting Mu in kN instead of kN·m

Key phrases to include

  • 1.2D + 1.6L
  • LRFD Combo 2
  • wu = 1.2(12) + 1.6(6)
  • Mu = wuL²/8
  • kN·m

An interior column supports a tributary area of 7 m × 7 m = 49 m². Dead load intensity = 5 kPa, live load intensity = 3 kPa. Compute the LRFD factored axial load Pu and the ASD service axial load P. (3 marks)

Tributary Area — Column Axial Loadmediumnumerical3 marks

Examiner tip

Always compute PD and PL separately before applying load factors. Applying a single factor to the combined service load is a common and serious error that loses 2 marks.

Model answer

Given:
Tributary area, At = 49 m²
qD = 5 kPa; qL = 3 kPa

Step 1 — Service axial loads:
PD = qD × At = 5 × 49 = 245 kN
PL = qL × At = 3 × 49 = 147 kN

Step 2 — ASD service combination (NSCP 2015 ASD Combo 2: D + L):
P = PD + PL = 245 + 147 = 392 kN

Step 3 — LRFD factored combination (NSCP 2015 LRFD Combo 2: 1.2D + 1.6L):
Pu = 1.2PD + 1.6PL
= 1.2(245) + 1.6(147)
= 294.0 + 235.2
= 529.2 kN

Also check LRFD Combo 1: 1.4PD = 1.4(245) = 343 kN < 529.2 kN → Combo 2 governs.

∴ ASD service load P = 392 kN; LRFD factored load Pu = 529.2 kN

Answer structure

  • Step 1: Compute service loads PD and PL using P = q × At with units [1 mark]
  • Step 2: ASD combination P = PD + PL = 392 kN [1 mark]
  • Step 3: LRFD combination Pu = 1.2PD + 1.6PL = 529.2 kN, verify Combo 1 does not govern [1 mark]

Scoring breakdown

1 mark

Criteria

PD = 245 kN and PL = 147 kN correctly calculated using P = q × At

1 mark

Criteria

ASD service load P = 392 kN using D + L

1 mark

Criteria

LRFD Pu = 529.2 kN using 1.2D + 1.6L, with Combo 1 check shown

Common mark deductions

  • Using At = 7 × 7/4 (quarter area) — this is wrong; interior column takes full tributary area
  • Skipping the Combo 1 check (1.4D) — examiners look for this comparison
  • Computing Pu = 1.2(392) — incorrectly applying load factor to the combined service load instead of to D and L separately

Key phrases to include

  • P = q × At
  • tributary area
  • ASD Combo 2: D + L
  • LRFD Combo 2: 1.2D + 1.6L
  • governs
  • kN

A column carries the following service loads: Dead load D = 200 kN, Live load L = 120 kN, and lateral Wind load W = ±90 kN. Evaluate all applicable NSCP 2015 LRFD combinations and determine the governing factored axial load Pu. (3 marks)

NSCP LRFD — Wind Load Combinationshardnumerical3 marks

Examiner tip

For any problem with lateral loads (W or E), ALWAYS write out Combo 6 (LRFD) or Combo 7 (ASD) even if it seems obvious dead load won't be overcome. The examiner's rubric specifically checks for this.

Model answer

Given: D = 200 kN, L = 120 kN, W = ±90 kN (axial; + = compression, − = tension/uplift)

Evaluate LRFD Combinations (NSCP 2015 Section 203.3):

Combo 1: U = 1.4D = 1.4(200) = 280.0 kN (compression)
Combo 2: U = 1.2D + 1.6L = 1.2(200) + 1.6(120) = 240 + 192 = 432.0 kN (compression)
Combo 4: U = 1.2D + 1.0W + 1.0L
= 1.2(200) + 1.0(+90) + 1.0(120) = 240 + 90 + 120 = 450.0 kN (compression, W additive)
= 1.2(200) + 1.0(−90) + 1.0(120) = 240 − 90 + 120 = 270.0 kN (compression, W subtractive)
Combo 6: U = 0.9D + 1.0W
= 0.9(200) + 1.0(+90) = 180 + 90 = 270.0 kN (compression)
= 0.9(200) + 1.0(−90) = 180 − 90 = 90.0 kN (compression; check for net tension if W > 0.9D → not the case here)

Comparison:
Maximum compression: Combo 4 (+W) → Pu = 450.0 kN ← GOVERNS for compression design
Minimum (possible uplift check): Combo 6 (−W) → Pu = 90.0 kN (still compression, no net uplift)

∴ Governing Pu = 450.0 kN (compression), from LRFD Combo 4 with additive wind.

Answer structure

  • Step 1: Evaluate gravity-only combos (1 and 2) [1 mark]
  • Step 2: Evaluate Combo 4 (1.2D + 1.0W + 1.0L) for both ±W [1 mark]
  • Step 3: Evaluate Combo 6 (0.9D + 1.0W) for uplift check, identify governing value [1 mark]

Scoring breakdown

1 mark

Criteria

Correct evaluation of Combos 1 and 2 (280 kN and 432 kN)

1 mark

Criteria

Correct evaluation of Combo 4 for both +W and −W scenarios (450 kN and 270 kN)

1 mark

Criteria

Correct evaluation of Combo 6 (0.9D ± W), identification of governing Pu = 450 kN, and note on uplift check

Common mark deductions

  • Evaluating only one sign of wind load — both +W and −W must be checked
  • Omitting Combo 6 (0.9D + 1.0W) — the most commonly missed combination on board exams
  • Selecting Combo 2 as governing without checking wind combinations

Key phrases to include

  • 0.9D + 1.0W
  • uplift check
  • ±W
  • LRFD Combo 4
  • governs
  • 450.0 kN

Explain, with reference to NSCP 2015, why earthquake load E frequently governs structural design in the Philippines. (3 marks)

Earthquake Load — Philippine Contextmediumshort answer3 marks

Examiner tip

This 3-mark conceptual question follows a classic Why-What-How structure: Why is E large in PH? What does the code say? How does it affect design? One paragraph per mark point is ideal.

Model answer

The Philippines lies along the Pacific Ring of Fire and is one of the most seismically active countries in the world, situated at the convergence of the Philippine Sea Plate, the Eurasian Plate, and the Sunda Plate. Consequently, NSCP 2015 assigns high seismic zone factors and requires buildings to be designed for significant lateral seismic forces.

From a load combination standpoint, the NSCP 2015 LRFD combination involving earthquake is:
U = 1.2D + 1.0E + 1.0L (Combo 5)
U = 0.9D + 1.0E (Combo 7 — for uplift/overturning due to seismic)

Unlike wind, which varies with height and exposure, seismic force E is derived from the building's mass and the ground acceleration (per NSCP 2015 Section 208), meaning heavier structures attract larger seismic forces. In most Philippine buildings, the combination with E produces the largest lateral force demand on columns, shear walls, and connections, causing these combinations to govern over gravity-only or wind combinations in lateral design. This is why Philippine structural engineers must prioritise seismic design in proportioning lateral force-resisting systems.

Answer structure

  • Point 1: Geographic/tectonic context — Philippines on the Ring of Fire, high seismicity [1 mark]
  • Point 2: Cite the NSCP LRFD combinations involving E (Combos 5 and 7) [1 mark]
  • Point 3: Explain why E governs — mass-proportional force, high ground accelerations, lateral demand on structural members [1 mark]

Scoring breakdown

1 mark

Criteria

Geographic or tectonic basis for high seismicity in the Philippines (Ring of Fire, plate tectonics, or equivalent)

1 mark

Criteria

Correct citation of NSCP LRFD load combination(s) involving E with correct factors

1 mark

Criteria

Explanation of why E governs: mass-proportional nature of seismic force, large ground accelerations, or predominance in lateral design

Common mark deductions

  • Saying 'earthquake load is large' without explaining why (tectonic setting) — lacks technical justification
  • Citing the correct combination but with wrong factors (e.g., 1.6E) — loses the combination mark
  • Discussing seismic design in general without linking back to load combinations

Key phrases to include

  • Ring of Fire
  • seismically active
  • 1.2D + 1.0E + 1.0L
  • 0.9D + 1.0E
  • lateral force
  • NSCP 2015 Section 208
  • governs

A floor beam (simply supported, span L = 7 m) carries area loads qD = 3.5 kPa and qL = 2.0 kPa on a tributary width of 4 m. Determine: (a) the service line loads, (b) the LRFD factored line load wu, and (c) the factored midspan moment Mu. (5 marks)

Tributary Area + LRFD Combinations — Beam Analysismediumnumerical5 marks

Examiner tip

Structure your answer with clear part labels (a), (b), (c). Examiners mark part by part, so a mistake in (b) does not cost you marks in (c) if you carry forward your wu value correctly and show the moment formula.

Model answer

Given:
Span, L = 7 m
Tributary width, b = 4 m
Area dead load, qD = 3.5 kPa
Area live load, qL = 2.0 kPa

(a) Service Line Loads:
wD = qD × b = 3.5 × 4 = 14.0 kN/m
wL = qL × b = 2.0 × 4 = 8.0 kN/m
Total service load (ASD, D + L): w = 14.0 + 8.0 = 22.0 kN/m

(b) LRFD Factored Line Load:
Check Combo 1: 1.4wD = 1.4(14.0) = 19.6 kN/m
Check Combo 2: wu = 1.2wD + 1.6wL
= 1.2(14.0) + 1.6(8.0)
= 16.8 + 12.8
= 29.6 kN/m ← GOVERNS (Combo 2 > Combo 1)

∴ wu = 29.6 kN/m

(c) Factored Midspan Moment:
For a simply supported beam with UDL:
Mu = wuL²/8
= 29.6 × (7)²/8
= 29.6 × 49/8
= 1,450.4/8
= 181.3 kN·m

Summary:
(a) wD = 14.0 kN/m, wL = 8.0 kN/m, w_service = 22.0 kN/m
(b) wu = 29.6 kN/m (LRFD Combo 2 governs)
(c) Mu = 181.3 kN·m

Answer structure

  • Part (a): Apply w = q × b to get wD and wL, state service total (ASD) [1.5 marks]
  • Part (b): Evaluate LRFD Combo 1 and Combo 2, identify governing wu [2 marks]
  • Part (c): Apply Mu = wuL²/8 with correct substitution and units [1.5 marks]

Scoring breakdown

1 mark

Criteria

wD = 14.0 kN/m and wL = 8.0 kN/m correctly computed (w = q × b demonstrated)

0.5 marks

Criteria

Service total w = 22.0 kN/m stated

1 mark

Criteria

Combo 1 (1.4D = 19.6 kN/m) evaluated and shown

1 mark

Criteria

Combo 2 (1.2D + 1.6L = 29.6 kN/m) correctly computed and identified as governing

1 mark

Criteria

Mu = wuL²/8 = 181.3 kN·m correctly computed with formula and units

0.5 marks

Criteria

Clear summary or boxed final answers provided

Common mark deductions

  • Skipping Combo 1 check — the examiner expects both combinations to be evaluated
  • Using L = 7 m without squaring in the moment formula (computing 29.6 × 7 / 8 instead of 29.6 × 49 / 8)
  • Reporting the moment in kN/m instead of kN·m — dimensional error deducts half a mark

Key phrases to include

  • w = q × b
  • tributary width
  • Combo 1: 1.4D
  • Combo 2: 1.2D + 1.6L
  • governs
  • Mu = wuL²/8
  • kN/m
  • kN·m

A structural column carries: Dead load D = 300 kN, Live load L = 180 kN, Roof live load Lr = 50 kN, and no wind or seismic. Apply all relevant NSCP 2015 LRFD gravity combinations and determine the governing Pu. (5 marks)

LRFD Gravity Combinations with Roof Live Loadhardnumerical5 marks

Examiner tip

The Lr factor swap between Combo 2 (0.5Lr companion) and Combo 3 (1.6Lr primary) is a classic board-exam trap. Write out both combinations fully to demonstrate you understand the distinction.

Model answer

Given: D = 300 kN, L = 180 kN, Lr = 50 kN (roof live), W = 0, E = 0

NSCP 2015 LRFD Gravity Combinations (Section 203.3):

Combo 1: U = 1.4D
= 1.4(300) = 420.0 kN

Combo 2: U = 1.2D + 1.6L + 0.5Lr [since only Lr is present, use 0.5Lr]
= 1.2(300) + 1.6(180) + 0.5(50)
= 360 + 288 + 25
= 673.0 kN

Combo 3: U = 1.2D + 1.6Lr + 1.0L [f1 = 1.0 as conservative default]
= 1.2(300) + 1.6(50) + 1.0(180)
= 360 + 80 + 180
= 620.0 kN
(Alternative using 0.5L for non-assembly occupancy: 1.2(300) + 1.6(50) + 0.5(180) = 360 + 80 + 90 = 530 kN)

Comparison:
Combo 1: 420.0 kN
Combo 2: 673.0 kN ← MAXIMUM
Combo 3: 620.0 kN (conservative, f1 = 1.0)

∴ Governing Pu = 673.0 kN from LRFD Combo 2 (1.2D + 1.6L + 0.5Lr).

Answer structure

  • Identify applicable combinations: Combos 1, 2, and 3 (gravity only, no wind/seismic) [1 mark]
  • Correctly evaluate Combo 1: U = 1.4D = 420.0 kN [1 mark]
  • Correctly evaluate Combo 2: U = 1.2D + 1.6L + 0.5Lr = 673.0 kN [1.5 marks]
  • Correctly evaluate Combo 3: U = 1.2D + 1.6Lr + 1.0L = 620.0 kN [1 mark]
  • Compare all three results and state governing Pu = 673.0 kN [0.5 mark]

Scoring breakdown

1 mark

Criteria

Correct identification of applicable LRFD combinations (1, 2, 3) and omission of wind/seismic combinations

1 mark

Criteria

Combo 1: U = 1.4(300) = 420.0 kN

1.5 marks

Criteria

Combo 2: correct factors 1.2D + 1.6L + 0.5Lr and result 673.0 kN

1 mark

Criteria

Combo 3: correct factors 1.2D + 1.6Lr + (1.0 or 0.5)L with reasoned choice of f1 factor

0.5 marks

Criteria

Correct identification of governing combination and final answer Pu = 673.0 kN

Common mark deductions

  • Using the wrong factor on Lr in Combo 2 (using 1.6Lr instead of 0.5Lr in Combo 2) — the 0.5 companion factor applies when Lr accompanies 1.6L
  • Evaluating only Combo 2 and skipping Combo 3 — both must be compared
  • Confusing Lr (roof live load) with L (floor live load) — these take different positions in different combinations

Key phrases to include

  • 1.4D
  • 1.2D + 1.6L + 0.5Lr
  • 1.2D + 1.6Lr + 1.0L
  • f1 factor
  • governs
  • 673.0 kN
  • NSCP 2015 Combo 2

Explain the concept of tributary area and show how it is used to determine the design axial load on an edge column versus an interior column in a regular floor grid. (3 marks)

Tributary Area — Column Load Distributionmediumshort answer3 marks

Examiner tip

A small sketch showing a 3×3 column grid with tributary areas shaded for interior, edge, and corner columns communicates the concept instantly and can substitute for a lengthy written explanation — it also earns the diagram bonus mark if the rubric allows.

Model answer

Tributary area is the floor area that is assumed to channel its load to a particular structural member — it is bounded by lines drawn midway between adjacent parallel members.

For a regular bay with column spacing Sx in the x-direction and Sy in the y-direction:

  • Interior column: receives load from all four surrounding bays → tributary area = Sx × Sy (full bay area).
  • Edge column (on one exterior face): receives load from one full span in one direction and a half-span in the other → tributary area = (Sx/2) × Sy or Sx × (Sy/2) depending on which edge.
  • Corner column: receives only a quarter-bay contribution from each adjacent bay → tributary area = (Sx/2) × (Sy/2).

Design axial load: P = q × At, where q is the area load intensity (kPa) and At is the tributary area.

Example: Sx = Sy = 6 m, q = 8 kPa
Interior: At = 36 m² → P = 288 kN
Edge: At = 18 m² → P = 144 kN
Corner: At = 9 m² → P = 72 kN

This shows that interior columns carry the largest axial load and must be proportioned accordingly.

Answer structure

  • Define tributary area clearly with the midpoint-boundary concept [1 mark]
  • Compare interior vs. edge vs. corner column tributary areas with correct fractions [1 mark]
  • Apply P = q × At with a numerical example showing the difference [1 mark]

Scoring breakdown

1 mark

Criteria

Correct definition of tributary area using midpoint boundaries, stated in own words

1 mark

Criteria

Correct tributary area fractions for interior (full), edge (half in one direction), and corner (quarter) columns

1 mark

Criteria

Application of P = q × At with a numerical or symbolic example showing quantitative difference

Common mark deductions

  • Stating tributary area without explaining the midpoint-boundary rule — too vague
  • Giving only the interior column case without comparing to edge/corner columns
  • Not applying the formula P = q × At with an example — explanation alone is insufficient for full marks

Key phrases to include

  • tributary area
  • midway between adjacent members
  • interior column: Sx × Sy
  • edge column: Sx/2 × Sy
  • corner column: Sx/2 × Sy/2
  • P = q × At

What is the minimum floor live load (kPa) specified by NSCP 2015 for (a) residential occupancy and (b) a school classroom? Why are live loads specified by occupancy rather than calculated from first principles?

Live Load Values by Occupancyeasyshort answer2 marks

Examiner tip

Board questions often ask for code table values — memorise at least residential (1.9 kPa), office (2.4 kPa), corridors (4.8 kPa), and storage (5.0–12 kPa) live loads from NSCP Table 205-1.

Model answer

(a) Residential occupancy minimum live load: 1.9 kPa (NSCP 2015 Table 205-1)
(b) School classroom minimum live load: 1.9–2.9 kPa depending on the specific classroom type (e.g., 1.9 kPa for typical classrooms; up to 4.8 kPa for areas with fixed seats and possible crowd loading — NSCP 2015 Table 205-1)

Live loads are specified by occupancy because the actual distribution and magnitude of people, furniture, and movable equipment are highly variable and cannot be determined exactly at the design stage. Code-specified minimum values represent statistically derived envelopes of the maximum loads expected over the life of the building for a given use, ensuring consistent and conservative design without requiring building-by-building occupancy surveys.

Answer structure

  • Part (a): State residential live load = 1.9 kPa with code table reference [0.5 mark]
  • Part (b): State classroom live load range 1.9–2.9 kPa with code table reference [0.5 mark]
  • Explain why occupancy-based specification: statistical nature, variability, design-stage uncertainty [1 mark]

Scoring breakdown

0.5 marks

Criteria

Residential live load: 1.9 kPa stated correctly

0.5 marks

Criteria

Classroom live load in the range 1.9–2.9 kPa or a specific NSCP table value cited

1 mark

Criteria

Correct justification: variability of occupancy loads, statistical basis, impossibility of exact calculation at design stage

Common mark deductions

  • Giving an incorrect value for residential live load (e.g., 2.5 kPa) — no mark for that part
  • Explaining only what live loads are instead of why they are specified by occupancy

Key phrases to include

  • 1.9 kPa
  • NSCP 2015 Table 205-1
  • variable
  • statistical
  • occupancy
  • design stage uncertainty

Using NSCP 2015 ASD load combinations, a beam has wD = 10 kN/m, wL = 8 kN/m, and a roof live load wLr = 3 kN/m (span 7 m, simply supported). Determine the ASD governing service UDL and the corresponding design moment. (5 marks)

NSCP ASD Load Combinationshardnumerical5 marks

Examiner tip

ASD Combo 4 (D + 0.75L + 0.75Lr) is often overlooked because reviewees memorise only D + L as the governing gravity case. Always run all four ASD gravity combos when Lr is given.

Model answer

Given: wD = 10 kN/m, wL = 8 kN/m, wLr = 3 kN/m, L = 7 m, simply supported

NSCP 2015 ASD Load Combinations (Section 203.4):

Combo 1: w = D = 10.0 kN/m
Combo 2: w = D + L = 10 + 8 = 18.0 kN/m
Combo 3: w = D + Lr = 10 + 3 = 13.0 kN/m
Combo 4: w = D + 0.75L + 0.75Lr
= 10 + 0.75(8) + 0.75(3)
= 10 + 6.0 + 2.25
= 18.25 kN/m
(Note: Combos 5, 6, 7 involve W or E which are zero here → not applicable)

Comparison:
Combo 1: 10.0 kN/m
Combo 2: 18.0 kN/m
Combo 3: 13.0 kN/m
Combo 4: 18.25 kN/m ← GOVERNS

∴ Governing ASD design UDL = 18.25 kN/m

Design moment (simply supported, UDL):
M = wL²/8
= 18.25 × (7)²/8
= 18.25 × 49/8
= 894.25/8
= 111.8 kN·m

∴ ASD design moment M = 111.8 kN·m

Answer structure

  • Identify applicable ASD combinations (1–4, omit 5–7 due to W = E = 0) [1 mark]
  • Evaluate Combo 1 (D) and Combo 2 (D + L) correctly [1 mark]
  • Evaluate Combo 3 (D + Lr) and Combo 4 (D + 0.75L + 0.75Lr) correctly [1.5 marks]
  • Identify governing combination as Combo 4 at 18.25 kN/m [0.5 mark]
  • Compute design moment M = wL²/8 = 111.8 kN·m with units [1 mark]

Scoring breakdown

1 mark

Criteria

Correct identification of applicable combinations (1–4) and proper exclusion of wind/seismic combos

1 mark

Criteria

Correct Combo 1 (10.0 kN/m) and Combo 2 (18.0 kN/m)

1.5 marks

Criteria

Correct Combo 3 (13.0 kN/m) and Combo 4 (18.25 kN/m) with 0.75 factors shown

0.5 marks

Criteria

Correct identification of Combo 4 as governing

1 mark

Criteria

M = 111.8 kN·m computed correctly using governing load with formula shown

Common mark deductions

  • Using LRFD factors (1.2D, 1.6L) in an ASD problem — fundamental conceptual error, no marks for those steps
  • Not evaluating Combo 4 and assuming Combo 2 always governs in ASD — Combo 4 (0.75 companions) can govern when Lr is present
  • Computing M = wL/8 without squaring L

Key phrases to include

  • ASD Combo 4
  • D + 0.75L + 0.75Lr
  • 18.25 kN/m
  • governs
  • M = wL²/8
  • 111.8 kN·m
  • NSCP 2015

State the NSCP 2015 provision on the companion live-load factor f1 in LRFD combinations 3–5, and identify when f1 = 1.0 versus f1 = 0.5 applies. (2 marks)

LRFD Companion Live-Load Factor f1mediumshort answer2 marks

Examiner tip

The f1 factor is a small but frequently tested NSCP detail. Memorise the trigger conditions: assembly, garages, or L > 4.8 kPa → f1 = 1.0. Everything else → f1 = 0.5.

Model answer

In NSCP 2015 LRFD Combinations 3, 4, and 5 (where L appears alongside a primary variable load such as Lr, W, or E), the live load term is written as f1L, where f1 is the companion live-load factor:

  • f1 = 1.0 for: (a) places of public assembly (e.g., auditoriums, stadia, gymnasiums), (b) garages and parking structures, and (c) any occupancy where the design live load L > 4.8 kPa.
  • f1 = 0.5 for: all other occupancies (e.g., typical offices, residences, classrooms).

Rationale: For high-occupancy or storage areas where full live load is likely to coexist with the primary variable load event, f1 = 1.0 applies. For typical occupancies, statistical evidence shows that full L and full Lr/W/E are unlikely to occur simultaneously, so the reduced factor f1 = 0.5 is used. In practice, many review centres default to f1 = 1.0 as the conservative value.

Answer structure

  • Point 1: State that f1 = 1.0 applies to assembly areas, garages, and L > 4.8 kPa [1 mark]
  • Point 2: State that f1 = 0.5 applies to all other occupancies, with a brief rationale [1 mark]

Scoring breakdown

1 mark

Criteria

Correct conditions for f1 = 1.0: assembly, garages, L > 4.8 kPa (at least two conditions stated)

1 mark

Criteria

Correct statement that f1 = 0.5 for all other occupancies, with statistical rationale (simultaneous occurrence)

Common mark deductions

  • Stating f1 = 0.5 always — ignoring the 1.0 condition for assembly/garages
  • Confusing f1 with the load factor on L in Combo 2 (which is always 1.6, not f1)

Key phrases to include

  • f1 = 1.0
  • f1 = 0.5
  • assembly areas
  • garages
  • L > 4.8 kPa
  • companion factor
  • simultaneous occurrence

Mark wise strategy

Recall and precision. The answer is a single definition, a code value, a formula, or a one-line conclusion. Write it once, clearly, with correct terminology. Do not elaborate unnecessarily.

1 mark1–2 lines (or one equation)1–2 minutes

Do

  • State the key term or code-specified value with correct units
  • Write code section or table number if the question is about a code provision
  • Use correct symbolic notation (e.g., U = 1.2D + 1.6L)
  • Underline or box the answer to make it easy to find

Don't

  • Do not write paragraphs — examiners do not award extra marks for excess explanation at 1-mark level
  • Do not leave blank — a partially correct answer still earns the mark if the core concept is present
  • Do not use colloquial language — maintain technical precision

Two distinct points or two calculation steps, each worth 1 mark. For numerical questions: show the formula, substitute, and state the answer. For conceptual questions: make two clearly distinguishable, technically precise statements.

2 marks3–6 lines or two steps with working3–5 minutes

Do

  • Label your two main points clearly (Point 1, Point 2 or Step 1, Step 2)
  • Show formula before substituting numbers
  • Include correct units at every step for numerical problems
  • For comparison questions (e.g., LRFD vs ASD), use a parallel structure

Don't

  • Do not merge both points into one long paragraph — examiners need to identify two separate mark-earning elements
  • Do not skip the formula step and jump to the answer — process marks are awarded
  • Do not omit units on line loads (kN/m) or moments (kN·m)

Three distinct mark-earning elements: typically Data/Given → Process/Formula → Result for numerical; or Context → Code Provision → Engineering Implication for conceptual. Structure your answer with clear headings or numbered steps.

3 marksHalf a page; 3 clear steps or paragraphs with calculation or explanation6–10 minutes

Do

  • Start with a Given/Required block for numerical problems — organise data before computing
  • Evaluate all relevant combinations (not just one) when a load combination question is asked
  • State the governing case explicitly: 'Combo X governs because it gives the largest value'
  • Cite NSCP 2015 section numbers to demonstrate code knowledge

Don't

  • Do not skip intermediate steps — partial marks are awarded for correct method even if the final number is wrong
  • Do not evaluate only one load combination when multiple combinations are required
  • Do not mix LRFD and ASD approaches within a single solution

Extended multi-step numerical or analytical answer. Plan your structure before writing: (a) identify data, (b) write all applicable combinations, (c) evaluate each, (d) identify governing, (e) compute final design quantity. Each of these is typically worth 1 mark. Check-back and double-check units before finalising.

5 marksFull page; multiple steps with formulas, substitutions, comparisons, and a summary12–18 minutes

Do

  • Use a systematic tabular or list format to present multiple load combinations for easy comparison
  • Show all applicable combinations even if they obviously do not govern — the rubric often requires this
  • Clearly label the final governing value and summarise all sub-results in a conclusion block
  • Write formulas in standard notation first (U = 1.2D + 1.6L), then substitute and compute
  • Check ± for wind or seismic cases — both signs must be evaluated

Don't

  • Do not skip Combo 1 (1.4D) in LRFD or Combo 1 (D alone) in ASD — they carry marks even if they do not govern
  • Do not apply factored loads to ASD allowable capacities or vice versa — this is a critical conceptual error
  • Do not omit the uplift check (0.9D + 1.0W or 0.6D + 0.6W) when W is given
  • Do not round intermediate values — carry at least 3 significant figures through the calculation

General answer writing tips

  • Always state the governing code reference (e.g., 'per NSCP 2015 Section 203') when citing load combinations or load factors — examiners reward explicit code literacy.
  • Write load combinations in full symbolic form first (e.g., U = 1.2D + 1.6L), then substitute numerical values — never skip straight to numbers without showing the formula.
  • Include units at every step of the calculation (kPa, kN/m, kN·m) — a correct numerical answer with missing or wrong units typically loses at least one mark.
  • For tributary area problems, clearly sketch or state the tributary width/area before computing — this demonstrates methodology even if you make an arithmetic error.
  • Distinguish LRFD and ASD explicitly: label factored loads as Pu, Mu, Wu and service loads as P, M, w — mixing notation signals conceptual confusion to the examiner.
  • In multi-combination problems, evaluate ALL relevant combinations and explicitly state which one governs — do not just compute one and assume it is the worst.
  • For uplift/overturning questions, always check the 0.9D + 1.0W (LRFD) or 0.6D + 0.6W (ASD) combination — this is a classic board-exam trap and omitting it loses marks.
  • End every numerical answer with a boxed or underlined final value and a concluding statement (e.g., 'Therefore, the factored design moment Mu = 108 kN·m') — this signals completeness to the examiner.

Diagrams

NSCP Load Types and Combinations — Master Overview

A comprehensive mind map organising all NSCP load types, tributary area concepts, LRFD and ASD combinations, and key design concepts. Use this as a study reference to see how all topics in the chapter interconnect before practising individual templates.

Step-by-Step Procedure for LRFD Load Combination Problems

A decision-flow diagram showing the systematic procedure for LRFD load combination problems. Students follow this flowchart to ensure no applicable combination is missed, particularly the critical uplift combinations (Combo 6 and 7) which are commonly omitted in board exams.

Tributary Area Determination for Different Column Positions

A flowchart illustrating how tributary area is determined based on column position (interior, edge, or corner) in a regular grid. This visual directly supports Template T12 and helps students avoid the common error of using incorrect tributary fractions.

Distribution of NSCP LRFD Load Combination Types by Design Scenario

A pie chart showing the approximate distribution of NSCP LRFD load combination scenarios encountered in board exams. Gravity-only combinations (D + L) appear most frequently, but wind and seismic combinations together represent 40% of exam problems — reinforcing why Combos 4–7 must be mastered.

LRFD vs ASD Design Philosophy Comparison

A side-by-side comparison flowchart of LRFD and ASD design philosophies. Shows how each approach handles loads (factored vs service) and resistance (φ-factor vs factor of safety), directly supporting Template T4 on the 2-mark differentiation question.

Loads and Load Combinations (NSCP) is chapter 6 of 6 in the Structural Theory & Analysis part of Super Tutor's CELE review. The Civil Engineer Licensure Examination is given by Professional Regulation Commission (PRC) — Board of Civil Engineering; its dates, format and passing rules are on the CELE page. See the CELE guide.

Study Loads and Load Combinations (NSCP) in the Super Tutor app

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