CELE Structural Theory & Analysis — Loads and Load Combinations (NSCP)Revision Notes

Formulas

Exam Tips

• NSCP Table 205-1 minimum live loads are frequently given in problems; memorize the common values: residential 1.9 kPa, office 2.4 kPa, assembly 4.8 kPa.
• When a problem says 'interior beam,' the tributary width = full bay spacing. 'Edge beam' = half bay spacing.
• For a two-way slab, tributary areas to beams are trapezoidal or triangular — if not specified, treat one-way and use s as the shorter direction.

Key Points

• Dead load (D): permanent, gravity, self-weight of structure plus all permanently attached items (finishes, fixed MEP, partitions). Highly predictable — lowest load factor in combinations.
• Live load (L): variable occupancy loads — people, furniture, movable equipment. NSCP Table 205-1 gives minimum values by occupancy: residential 1.9 kPa, office 2.4 kPa, classroom 1.9–2.9 kPa, assembly areas 4.8 kPa.
• Roof live load (Lr): temporary loads on roofs from maintenance workers and equipment. Distinct from ordinary live load.
• Wind load (W): depends on basic wind speed, exposure category, height above ground, and building shape/pressure coefficients (NSCP Section 207).
• Earthquake load (E): seismic; the Philippines lies along the Pacific Ring of Fire — E often GOVERNS lateral design, especially in Seismic Zones 4 and 4-A.
• Rain load (R): ponding from blocked drains on flat roofs.
• Snow (S): negligible in most Philippine locations; rarely tested.
• The companion action factor f1 for L in LRFD combos 3–5: f1 = 1.0 for assembly areas, garages, and L > 4.8 kPa; f1 = 0.5 for all other occupancies.

Definitions

Section Title

Load Types and Their Characteristics

Common Mistakes

• Using the full beam span as tributary width instead of the beam spacing (s) — the span is the length along the beam, the spacing is the tributary width perpendicular to it.
• Forgetting to add self-weight of the beam itself to the dead load when computing total wD.
• Using an occupancy live load for a roof — roof live load Lr is separate from floor LL.
• Confusing kPa (kN/m²) and kN/m — always check units when multiplying area loads by lengths.
• Assuming snow or rain govern in the Philippines — the seismic load E almost always governs lateral design in Philippine seismic zones.

Formulas

Exam Tips

• Always draw a quick floor plan sketch and mark tributary boundaries before computing any loads — this prevents errors on edge vs interior members.
• For columns: count the number of floors above, multiply the per-floor tributary load by the number of floors as a quick check.
• Beam self-weight can be estimated: for RC beams, unit weight of concrete γ = 23.5–24 kN/m³; beam self-weight per meter = γ × b × h.

Key Points

• Tributary area principle: each member carries the load from the region geometrically closer to it than to any other parallel member.
• Interior beam: tributary width = full spacing s (half-bay each side → total = s).
• Edge/perimeter beam: tributary width = s/2 (one-sided).
• Corner column: At = (s1/2)(s2/2). Interior column: At = s1 × s2. Edge column: At = (s1/2)(s2) or (s1)(s2/2). Always sketch the plan and draw the tributary boundaries.
• For a uniformly loaded simply supported beam: total reaction = (w × L)/2 at each support → this becomes the beam-end shear transferred to the girder or column.
• Multi-story buildings: column loads accumulate floor-by-floor (cumulative tributary load).

Definitions

Section Title

Tributary Area — Routing Loads to Members

Common Mistakes

• Assigning full bay spacing to an edge beam instead of half — this doubles the load on the edge beam erroneously.
• Forgetting to include the beam's own self-weight as part of dead load before computing wD.
• For a two-span continuous beam, using simple-beam tributary areas — the reactions differ; use proper analysis or moment distribution.
• Mixing up 'beam span' (along beam length) with 'beam spacing' (center-to-center distance between parallel beams).

Formulas

Exam Tips

• For gravity-only problems (no wind, no seismic): evaluate only U1, U2, U3, U4 (with W=0). U2 almost always governs when L is significant.
• For problems with wind: check U4 (1.2D+1.0W+1.0L) AND U6 (0.9D+1.0W). U6 may govern for uplift.
• Memorize the factored load factors: D gets 1.2 (or 0.9 for uplift), L gets 1.6 (primary) or 1.0 (companion), W and E get 1.0.
• Board exams often give wD and wL in kN/m and ask for wu and Mu — apply U2: wu = 1.2wD + 1.6wL, then Mu = wuL²/8.
• When the problem asks for 'design axial load' without specifying method, default to LRFD (Pu) unless ASD is explicitly stated.

Key Points

• LRFD (Load and Resistance Factor Design) amplifies loads with factors > 1.0 and reduces nominal strength with φ factors (φ < 1.0). The factored load demand ≤ factored strength.
• Gravity combinations are the most common in board problems. Combo 2 (1.2D + 1.6L) governs for most floor systems with large live loads.
• Combos 6 and 7 (0.9D + 1.0W and 0.9D + 1.0E) capture the UPLIFT condition — when wind or seismic acts upward and dead load resists it. The 0.9 factor reduces the 'helpful' dead load conservatively.
• The companion action factor f1 for L: use 1.0L for assembly areas (L > 4.8 kPa, garages); use 0.5L for all other occupancies in combos 3, 4, and 5.
• For seismic: E includes both horizontal (Eh) and vertical (Ev) components per NSCP Section 208. In simplified form, E = Eh ± Ev.
• Always evaluate ALL applicable combinations and use the one producing the most severe effect (max moment, max shear, max axial — can differ per combination).

Definitions

Section Title

LRFD Load Combinations (NSCP 2015)

Common Mistakes

• Applying only Combo U2 (1.2D + 1.6L) and ignoring the wind/seismic combinations — the problem may require checking all combos.
• Forgetting Combos U6 and U7 entirely — uplift/overturning can make an element go from compression to tension, requiring a completely different design.
• Using f₁ = 1.0L in combo U4 for a residential floor (correct f₁ = 0.5) — this overestimates the load but may cost accuracy points.
• Adding E and W in the same combination — NSCP does not combine E and W simultaneously; each is considered independently in its respective combination.
• Using LRFD factored loads (Pu, Mu, Vu) with allowable stress design tables — always match design method with the correct load combination set.

Formulas

Exam Tips

• ASD vs LRFD comparison for the same beam: LRFD always gives a larger design moment/force than ASD for the same loads — confirm this ratio to check your arithmetic.
• For a beam with wD = 12 and wL = 6 kN/m: LRFD wu = 24 kN/m; ASD w = 18 kN/m. The LRFD/ASD ratio ≈ 1.33, which is typical for D:L ≈ 2:1.
• When the exam says 'service loads' or 'working loads' — use ASD combinations. 'Factored loads' or 'design loads' — use LRFD.
• ASD Combo 5 uses 0.7E (not 1.0E). Many reviewees use 1.0E — this is ONLY for LRFD. The 0.7E in ASD is a calibration factor.

Key Points

• ASD (Allowable Stress Design) uses service (unfactored) loads; the structure is checked against an allowable stress = Fu/FS or Fy/FS where FS is a factor of safety.
• ASD Combo 1 (D alone) and Combo 2 (D + L) are the most common gravity ASD combinations.
• The 0.75 factor in Combos 4 and 6 reflects the reduced probability that all loads reach their maximums simultaneously.
• ASD uplift combos use 0.6D (analogous to LRFD 0.9D) — the reduced dead load is intentional for the stabilizing action.
• Wind appears as 0.6W and seismic as 0.7E in ASD — these are NOT the same W and E as in LRFD. The reduction factors make ASD wind/seismic comparable to LRFD in terms of reliability.
• Choose ONE design philosophy (LRFD or ASD) and apply it consistently — never mix factored and service loads in the same analysis.

Definitions

Section Title

ASD Load Combinations (NSCP 2015)

Common Mistakes

• Applying the 0.75 factor in ASD Combo 4 to the dead load — the 0.75 factor applies only to L and Lr/R, NOT to D.
• Confusing 0.6W (ASD) with 1.0W (LRFD) — ASD already applies the 0.6 factor to make wind comparable to LRFD in reliability.
• Using ASD service moment (M = wL²/8) directly in an LRFD design table — the design moment must match the design philosophy.
• Forgetting ASD-7 uplift combos (0.6D + 0.6W or 0.6D + 0.7E) when checking tension at foundations.

Formulas

Exam Tips

• QUICK CHECK for gravity beam: wu = 1.2wD + 1.6wL. If wD:wL ≈ 2:1, expect wu ≈ 1.33 × (wD + wL).
• For column with all loads (D, L, W): check at minimum: U2 (max compression, no wind), U4 (D+W+L, compression side), U6 (uplift, W opposite to D).
• Mu = wuL²/8 → Mu varies with L² — doubling the span quadruples the moment. This is why long-span beams are often the critical design element.
• Always state units clearly in the exam — kN·m for moment, kN for force, kN/m for line load, kPa for area load.

Key Points

• Example 1: Beam tributary line load — convert area loads to line loads using tributary width.
• Example 2: Factored beam moment (LRFD) — apply governing LRFD combo and compute Mu.
• Example 3: Column axial load (LRFD vs ASD) — compute Pu and P_service from tributary area loads.
• Example 4: Column with wind — check all relevant LRFD combos including uplift.
• Board exam problems typically present area loads (kPa) + geometry → ask for factored line load, design moment, or design axial force.

Definitions

Section Title

Worked Board-Style Examples

Common Mistakes

• Using M = wL²/8 for a continuous beam — this formula is ONLY for simply supported beams. For continuous beams, use moment coefficients or matrix methods.
• Forgetting that the beam's own self-weight contributes to wD — problems may give slab dead load but expect you to add beam self-weight.
• For columns with wind: students often check only U2 (gravity) and U4 (gravity + wind compression) but miss U6 (0.9D + W for potential uplift or tension).