Reinforced Concrete Columns - Cheat Sheet
Your 30-minute final review for RC column design, capacity calculations, interaction diagrams, and slenderness checks. Covers NSCP 2015 and ACI 318 limits.
Axial Capacity of Short Columns
Formulas
P₀ = 0.85f'c(Ag - Ast) + fyAst
Meaning
P₀ = nominal pure-axial strength (N); f'c = concrete strength (MPa); Ag = gross cross-sectional area (mm²); Ast = total longitudinal steel area (mm²); fy = steel yield strength (MPa)
Watch out
Use NET concrete area (Ag − Ast), NOT Ag alone. Steel contributes at fy, not at 0.85fy
When to use
First step: calculate maximum possible axial load before code cap and strength reduction
φPn,max = 0.80 × 0.65 × P₀ (tied column)
Meaning
φ = 0.65 (compression-controlled); 0.80 = code cap for tied; design axial capacity in kN
Watch out
DO NOT use 0.75 or 0.85 for tied columns. The cap is always 0.80 for tied, 0.85 for spiral
When to use
Calculate final design axial capacity for tied rectangular or polygonal columns
φPn,max = 0.85 × 0.75 × P₀ (spiral column)
Meaning
φ = 0.75 (spiral); 0.85 = code cap for spiral; higher capacity reflects ductility gain
Watch out
Spiral columns get BOTH a higher φ (0.75 vs 0.65) AND higher cap (0.85 vs 0.80) — they are ~23% stronger
When to use
Calculate final design axial capacity for spiral/circular columns
ρg = Ast / Ag
Meaning
ρg = gross longitudinal steel ratio (dimensionless); must fall within 0.01 to 0.08
Watch out
Ratio 0.01 ≤ ρg ≤ 0.08; in lap-splice regions, often limited to 0.04 by practical detailing
When to use
Check reinforcement ratio compliance before finalizing column design
Common values
Value
28 MPa (common), 35 MPa (high-rise), 40+ MPa (special)
Symbol
f'c
Quantity
Concrete compressive strength (Philippines, typical)
Value
415 MPa (Grade 60 equivalent, most common)
Symbol
fy
Quantity
Steel yield strength (Philippines, standard)
Value
0.65
Symbol
φ
Quantity
Design reduction factor – tied columns
Value
0.75
Symbol
φ
Quantity
Design reduction factor – spiral columns
Value
0.80
Symbol
α (tied)
Quantity
Code cap multiplier – tied
Value
0.85
Symbol
α (spiral)
Quantity
Code cap multiplier – spiral
Important facts
- Nominal axial strength P₀ always assumes concentric load (e = 0); real columns have moment, so use interaction diagram
- Tied columns: minimum 4 bars; spirals: minimum 6 bars
- φ for columns is 0.65 (tied) or 0.75 (spiral) — NOT 0.90 like beams
- Design axial capacity = φPn,max = 0.52 P₀ (tied) or 0.6375 P₀ (spiral)
- Code caps usable load at 80% of nominal for tied, 85% for spiral to account for unavoidable eccentricity
- Longitudinal steel ratio 0.01 ≤ ρg ≤ 0.08 (NSCP 2015 Section 10.9)
- Spiral pitch (vertical distance per turn) typically 50–80 mm
- Concrete strength used in P₀ calculation is f'c (28 day), not reduced by any factor
Key definitions
Gross area (Ag)
Example
400 × 400 mm column = 160,000 mm²
Total concrete cross-sectional area including space occupied by steel bars.
Net concrete area
Example
If Ast = 4000 mm², net = 160,000 − 4000 = 156,000 mm²
Ag minus Ast; the actual concrete carrying compression.
Short column
Example
Typically kℓu/r ≤ 22 for unbraced or ≤ 40 for braced frames
Slenderness ratio kℓu/r is low enough that P-Δ effects are negligible; no moment magnification needed.
Compression-controlled failure
Example
Occurs above the balanced point on interaction diagram; φ = 0.65 (tied) or 0.75 (spiral)
Concrete crushes at εc = 0.003 before steel yields; brittle, low ductility.
Tied column
Example
8–25 mm bars with No. 10 tie hoops @ 300 mm spacing
Longitudinal bars held by individual tie hoops; rectangular, polygonal, or circular section.
Spiral column
Example
12–20 mm bars with 6 mm spiral pitch 60 mm
Longitudinal bars wrapped by continuous spiral reinforcement; always circular section.
Diagrams to know
- P₀ vs ρg curve (increases linearly with steel ratio)
- Design capacity reduction over section size (larger columns relative to load slightly less efficient)
- Tied vs spiral capacity comparison bar chart
Reinforcement Limits & Details
Formulas
ρs ≥ 0.45 × [(Ag / Ach) − 1] × (f'c / fyt)
Meaning
ρs = spiral reinforcement ratio; Ag = gross area; Ach = core area (to outside of spiral); f'c = concrete strength; fyt = spiral yield strength (capped at 700 MPa in NSCP)
Watch out
fyt is capped at 700 MPa even if higher-grade steel used; use Ach not Ag in the denominator
When to use
Calculate minimum spiral diameter and pitch to satisfy confinement requirements
Spacing limits – ties: ≤ 16db (longitudinal bar), ≤ 48db (tie bar), ≤ least column dimension
Meaning
db = diameter of longitudinal bar; tie size and spacing per NSCP 10.17.1
Watch out
Use LEAST (smallest) dimension for column; a 400 × 300 tied column uses 300 mm, not 400 mm
When to use
Detail tie hoops in tied columns; all three conditions must be satisfied
Spiral pitch s: ≤ 75 mm (typical max), ≥ 25 mm (practical min)
Meaning
s = vertical distance per spiral turn (mm); controls degree of confinement
Watch out
Smaller pitch = higher ρs = better confinement but more expensive; balance with ρs equation
When to use
Design spiral geometry to meet ρs requirement and provide adequate core confinement
Minimum bars: tied ≥ 4, spiral ≥ 6
Meaning
Absolute minimum for code compliance and practical cage rigidity
Watch out
Six bars in a circle are symmetrical (60° apart); four bars are less stable — use triangular or square layouts
When to use
Check before finalizing reinforcement detail in any column design
Common values
Value
10 mm (No. 10) or 12 mm (No. 12) diameter
Symbol
dB (ties)
Quantity
Typical tie size
Value
300 mm (ordinary), 100–150 mm (seismic)
Symbol
s (ties)
Quantity
Typical tie spacing
Value
6 mm, 8 mm
Symbol
dsp
Quantity
Typical spiral diameter
Value
50–75 mm
Symbol
s (spiral)
Quantity
Typical spiral pitch
Value
40 mm
Symbol
cc
Quantity
Minimum concrete cover (ordinary columns)
Important facts
- Spiral columns > tied columns in strength AND ductility; spiral provides radial confinement (Poisson effect) plus transverse shear
- Minimum cover: 40 mm typical (45 mm for exposed to weather per NSCP 7.7.3)
- Lap-splice length per NSCP 12.2: in columns, ld = (fy / (1.1 × √f'c)) × db for #25 and smaller bars
- Tied columns cheaper to build; spirals mandatory for seismic Zones 4 (high-risk) per RA 9389 (NBCP)
- Tie spacing ≤ 300 mm typical in ordinary moment-resistant frames; ≤ 100 mm in high-seismic regions
- Spiral pitch measured vertically; volume of one turn = spiral area × circumference of centerline
- For circular sections, spiral is vastly more efficient than ties because confinement is isotropic
- Longitudinal bars in spirals need NOT be continuous (unlike tied columns) — easier to lap at different heights
Key definitions
Longitudinal steel ratio (ρg)
Example
400 × 400 column with 8–25 mm bars: ρg = 3927 / 160,000 = 0.0245 ✓
Ast / Ag; must be 0.01 ≤ ρg ≤ 0.08 (reduced to 0.04 in lap-splice zones per NSCP).
Spiral reinforcement ratio (ρs)
Example
Typical ρs = 0.006 to 0.015 for circular column cores
Volume of spiral steel per volume of core concrete; governs confinement effectiveness.
Core area (Ach)
Example
For 500 mm diameter column with 40 mm cover: Ach ≈ π(500−2×40)²/4 ≈ 134,042 mm²
Area enclosed by the centerline of the spiral; used in ρs and confinement equations.
Tie hoop
Example
10 mm diameter ties spaced 250 mm vertically in a 400 mm square column
Individual closed reinforcement loop (usually #10 or #12 bar) confining longitudinal bars in tied columns.
Spiral reinforcement
Example
6 mm diameter spiral with 60 mm pitch in a 500 mm diameter column
Continuous helical reinforcement wrapping the core in circular/spiral columns; more effective than ties.
Diagrams to know
- Tied column detail: corner bars + ties (elevation and section)
- Spiral column detail: circular core with continuous helix (elevation and section)
- Tie spacing diagram showing dB, pitch, and least dimension constraint
Axial–Moment Interaction Diagram
Formulas
Interaction diagram: plot (Pn, Mn) pairs for every neutral-axis depth c
Meaning
Pn = axial strength; Mn = moment strength; c = distance from extreme compression fiber to neutral axis (mm); diagram boundary = locus of all feasible (Pn, Mn) combinations
Watch out
Use the φ-REDUCED diagram for design (not the nominal diagram); point (Pu, Mu) MUST be inside
When to use
Check if factored load (Pu, Mu) falls within the reduced (φ-adjusted) diagram; if yes, section is safe
Pure axial point: (P₀, 0) at top of diagram
Meaning
When M = 0 (concentric load), axial capacity = P₀ (before cap and φ reduction)
Watch out
Real design capacity is 0.80φP₀ (tied) or 0.85φP₀ (spiral), NOT P₀
When to use
Mark upper bound of interaction diagram
Balanced point: (Pb, Mb) where εc = 0.003 and εs = εy simultaneously
Meaning
Pb = axial capacity at balance (N); Mb = maximum moment capacity the section can develop; c = cb (balanced neutral axis depth)
Watch out
At balanced point, φ transitions (NSCP 10.3.4); above it φ ≤ 0.65 or 0.75, below it φ increases toward 0.90
When to use
Identifies transition from compression-controlled (above) to tension-controlled (below)
Pure flexure point: (0, Mn) at bottom of diagram
Meaning
When P = 0, column acts as a cantilever beam; Mn = moment capacity in pure bending
Watch out
φ in pure bending is 0.90 (tension-controlled), NOT 0.65 or 0.75
When to use
Mark lower bound of interaction diagram
Common values
Value
0.003 (εc,max)
Symbol
εc
Quantity
Concrete strain at crushing
Value
0.00207 (415 / 200,000)
Symbol
εy
Quantity
Steel strain at yield (Grade 415 MPa)
Value
200,000 MPa
Symbol
Es
Quantity
Steel modulus of elasticity
Value
0.005 (transition end), 0.002 (transition start)
Symbol
εt
Quantity
Balanced strain threshold for φ transition
Important facts
- No real column carries pure axial load; interaction diagram accounts for unavoidable eccentricity
- Diagram is symmetric in many cases (symmetric reinforcement) but NOT always (asymmetric layout or loading plane)
- Strain compatibility governs the shape: as c increases from bottom to top, Pn increases and Mn typically decreases
- Balanced point is the 'knee' of the diagram — largest moment for a given section
- Design point (Pu, Mu) must lie INSIDE the φ-reduced diagram, often with margin
- Contour lines of eccentricity (e = M/P) are straight lines radiating from origin; steep slope = small e, gentle slope = large e
- Biaxial bending (moments in two directions) requires 3D surface; uniaxial interaction diagram is 2D section through that surface
- Spiral columns plot higher on diagram (larger P for same M) due to confinement and higher φ
Key definitions
Interaction diagram
Example
Parabolic or polygonal curve from (P₀, 0) through (Pb, Mb) to (0, Mn)
Graphical plot of axial vs moment capacity locus; any (Pu, Mu) inside the diagram is safe.
Balanced failure
Example
At balanced point, concrete is at edge of failure AND steel just begins to yield — optimal stress state
Simultaneous crushing of concrete (εc = 0.003) and yielding of tension steel (εs = fy/Es); maximum moment capacity.
Compression-controlled region (above balanced point)
Example
High axial load with small moment; concrete crushes first
Net tensile strain in extreme tension fiber ≤ 0.002; failure brittle; φ = 0.65 or 0.75.
Tension-controlled region (below balanced point)
Example
Low axial load with large moment; steel yields first
Net tensile strain in extreme tension fiber ≥ 0.005; failure ductile; φ = 0.90.
Transition zone
Example
φ = 0.65 + 0.25(εt − 0.002) / 0.003 for sections with strain ≤ 0.005
Between compression and tension control (εt = 0.002 to 0.005); φ interpolates linearly per NSCP 10.3.4.
Diagrams to know
- Interaction diagram curve from (P₀, 0) → (Pb, Mb) → (0, Mn)
- Neutral-axis evolution sketch showing c at different load stages
- Strain diagram at balanced failure: εc = 0.003 (concrete) and εs = fy/Es (steel)
- Eccentricity contours (straight lines) overlaid on interaction diagram
Slenderness & Moment Magnification
Formulas
Slenderness ratio: λ = kℓu / r
Meaning
k = effective length factor (0.5 braced, 1.0 unbraced); ℓu = unsupported length (mm); r = radius of gyration = √(I/Ag) (mm)
Watch out
k = 1.0 for unbraced (sway) frames; k = 0.5–0.7 for braced (non-sway); neglecting k gives unconservative result
When to use
Check if column is short or slender; if λ exceeds code limit, use moment magnification
Short column threshold (braced frame): λ ≤ 34 − 12(M₁/M₂), max 40
Meaning
M₁ = smaller end moment; M₂ = larger end moment; if ratio close to 1, limit ≈ 22
Watch out
If column is unbraced (sway), use λ ≤ 22 (simpler); if braced, use the 34 − 12(M₁/M₂) formula but cap at 40
When to use
Determine if moment magnification is needed in a braced (non-sway) frame
Short column threshold (unbraced frame): λ ≤ 22
Meaning
Conservative rule for sway frames; if λ > 22, treat as slender and magnify moments
Watch out
λ > 22 in unbraced frame → moment magnification REQUIRED; ignoring this causes unsafe design
When to use
Quick check for unbraced frames; if λ exceeds 22, column is definitely slender
Moment magnifier (method 1): Mc = δb × Mb + δs × Ms
Meaning
δb = braced-frame magnifier; δs = sway magnifier; Mb = primary moment; Ms = sway moment; Mc = magnified moment
Watch out
This is a simplified form; exact method requires alignment charts and iterative solutions (often done by software)
When to use
Amplify moments in slender columns to account for P-δ and P-Δ effects
Approximate magnifier: Cm / (1 − Pu / (φPc))
Meaning
Cm = moment distribution coefficient; Pu = factored axial load; Pc = Euler buckling load; magnifies primary moment in braced frame
Watch out
Denominator (1 − Pu / φPc) becomes large if Pu >> φPc, suggesting column is very slender and close to buckling
When to use
Rough estimate for slender column moment magnification; Cm ≈ 0.6 to 0.8 for typical cases
Euler buckling load: Pc = π² EI / (kℓu)²
Meaning
EI = flexural stiffness; k, ℓu as above; Pc is the elastic buckling capacity
Watch out
EI must be reduced per NSCP (typically EI = 0.4 Ec Ig); use effective stiffness, not gross moment of inertia
When to use
Estimate criticality of slenderness; used in magnifier denominator
Common values
Value
0.5
Symbol
k
Quantity
Effective length factor – fixed-fixed (braced)
Value
1.0
Symbol
k
Quantity
Effective length factor – hinged-hinged (simple frame)
Value
2.0
Symbol
k
Quantity
Effective length factor – fixed-free (cantilever)
Value
22
Symbol
λ limit
Quantity
Short-column limit (unbraced frame)
Value
4700√f'c MPa, e.g., ~30,000 MPa for f'c = 28 MPa
Symbol
Ec
Quantity
Concrete elastic modulus (typical)
Value
0.4 (for both Ec and Es contributions)
Symbol
α (EI)
Quantity
Effective EI reduction factor (NSCP)
Important facts
- Slenderness check is MANDATORY before using nominal interaction diagram
- Braced frames (e.g., shear walls + moment frame) have k ≤ 0.7; unbraced frames k ≥ 1.0
- Moment magnification typically increases required column size by 10–30% depending on slenderness
- Radius of gyration r ≈ 0.3 × (least dimension) for rectangular sections (rough estimate)
- P-Δ effects become critical when Pu / φPc > 0.4 (denominator < 0.6); column is near buckling
- High-rise buildings in Philippines (Zone 4 seismic) must account for P-Δ; low-rise braced frames often skip it
- Moment magnification methods: (1) exact alignment charts, (2) simplified formulas, (3) FEA with P-Δ geometry
- NSCP 2015 Section 10.13 and 10.14 govern slender column design; ACI 318 uses similar approach
Key definitions
Slender column
Example
kℓu/r = 45 in an unbraced frame → slender, must use moment magnification
Column in which lateral deflection (P-Δ or P-δ) significantly reduces moment capacity; slenderness ratio exceeds code limit.
Short column
Example
kℓu/r = 18 in braced frame → short, use nominal interaction diagram
Column in which P-Δ effects are negligible; can neglect moment magnification; slenderness ratio within code limit.
Effective length factor (k)
Example
Hinged-hinged: k ≈ 1.0; fixed-fixed: k ≈ 0.5; fixed-free (cantilever): k ≈ 2.0
Adjustment to unsupported length accounting for end-support conditions; k = 0.5–0.7 (braced), k = 1.0–2.0 (unbraced).
Radius of gyration (r)
Example
For square 400 × 400: r = (400 × 400³ / 12) / (400 × 400) / √(...) ≈ 115 mm
r = √(I/Ag); property of cross-section reflecting how far centroidal area is distributed.
P-Δ effect (Delta-delta)
Example
Column sways Δ → additional moment P × Δ at section
Lateral deflection of column under P and moment, amplifying moment at mid-height; second-order effect within a floor.
P-delta effect (Delta-big-delta)
Example
Frame sways 10 mm sideways under wind → P × 10 mm moment added to each column
Story-level lateral sway under overall frame loading; amplifies moments in all columns of a story.
Diagrams to know
- Slenderness limit vs frame type graph (braced vs unbraced)
- Moment magnifier curve: 1/(1 − Pu/φPc) vs Pu/φPc
- Column deflection sketch showing P-Δ and P-delta contributions
Design Workflow & Common Exam Traps
Formulas
Design check sequence: (1) Calculate Ag & Ast → (2) Find P₀ → (3) Apply cap & φ → (4) Check ρg limits → (5) Check slenderness → (6) Check (Pu, Mu) vs interaction diagram
Meaning
Sequential steps ensuring safe, code-compliant column design
Watch out
Missing any step can lead to incorrect answer; slenderness check is easily overlooked
When to use
Exam question: 'Is this column safe?' — follow this checklist
Trap 1: Using P₀ directly instead of φPn,max = 0.52P₀ (tied) or 0.6375P₀ (spiral)
Meaning
Nominal strength ≠ design strength; must reduce by both cap (0.80 or 0.85) AND φ (0.65 or 0.75)
Watch out
Common exam mistake: reporting P₀ or 0.65P₀ instead of 0.52P₀
When to use
Every time you calculate axial capacity; easy to forget cap factor
Trap 2: Using gross area (Ag) instead of net concrete area (Ag − Ast) in concrete term
Meaning
P₀ = 0.85f'c(Ag − Ast) + fyAst; forgetting the minus sign doubles the concrete contribution
Watch out
Concrete carries only (Ag − Ast); steel at fy on full Ast. DO NOT use 0.85 on steel
When to use
Always in P₀ calculation; 20–30% of exam errors here
Trap 3: Confusing tied (φ = 0.65) with spiral (φ = 0.75) — or worse, using 0.90
Meaning
Columns are compression-controlled; φ ≠ 0.90. Tied = 0.65, spiral = 0.75, period
Watch out
Zero points if you use φ = 0.90 — automatic indicator of fundamental misunderstanding
When to use
Exam problem specifies tied or spiral; use correct φ
Important facts
- In exam, problems often give Pu (axial) and Mu (moment); you must check BOTH — axial alone is incomplete
- Many designers underestimate moment; actual P-M combinations from structural analysis are usually well above pure axial
- Reinforcement ratio ρg = 0.02 is common default; don't exceed 0.04 in lap-splice zones
- Tied columns dominate in residential/medium buildings; spirals in high-rise seismic zones (RA 9389)
- Minimum column size ≈ 300 mm × 300 mm (practical); 250 mm rarely used due to congestion
- Design for tied column always cheaper upfront; spiral pays off in seismic regions and high-rise efficiency
Key definitions
Design workflow
Example
Given Pu & Mu → assume column size → calculate Pn & Mn → check if (Pu, Mu) inside φ-reduced diagram
Systematic process from assumed dimensions → capacity calc → limit checks → interaction diagram verification.
Trial-and-error design
Example
Start 400 mm; if undersized, try 450 mm; if oversized, try 425 mm
Iterative process: guess size, check capacity, adjust, repeat until safe and economical.
Must remember
- P₀ = 0.85f'c(Ag − Ast) + fyAst — most critical formula; wrong net area is the #1 mistake
- φPn,max = 0.52P₀ (tied) or 0.6375P₀ (spiral) — always apply BOTH the cap (0.80 or 0.85) AND φ (0.65 or 0.75)
- 0.01 ≤ ρg ≤ 0.08 — mandatory limits; violating this is automatic failure in any section
- Columns are compression-controlled: φ = 0.65 (tied) or 0.75 (spiral), NEVER 0.90 — confusing this loses exam points
- Interaction diagram governs real design — pure axial capacity is useless without checking (Pu, Mu) vs the reduced diagram
- Slenderness ratio λ = kℓu/r — if λ exceeds code limit (22 unbraced, ~34 braced), moment magnification is MANDATORY
- Spiral columns are ~23% stronger (same materials) because cap = 0.85 vs 0.80 AND φ = 0.75 vs 0.65; also superior ductility
- Effective length factor k — k = 0.5–0.7 braced, k ≥ 1.0 unbraced; using wrong k changes slenderness check dramatically
- Balanced point on interaction diagram has maximum moment (Mb); above it compression-controlled (φ low), below it tension-controlled (φ high)
- Minimum bars: tied ≥ 4, spiral ≥ 6 — non-negotiable; fewer bars = code violation and poor cage rigidity
Last minute tips
- Always check slenderness first — if λ > limit, column is slender and moments must be magnified before using interaction diagram; skipping this is a common exam trap
- Use net concrete area (Ag − Ast), not Ag — this single mistake can inflate P₀ by 20–30%; write it out clearly to avoid careless error under time pressure
- Verify ρg AFTER finalizing steel — if ρg falls outside 0.01–0.08, redesign; don't report an answer with bad ρg; also check ρg ≤ 0.04 in lap-splice zones
- Read problem carefully for tied vs. spiral — wrong φ/cap is an instant major deduction; confirm section type before calculating
- Plot (Pu, Mu) on interaction diagram — even if not to scale, visually confirm the factored point lies inside the φ-reduced boundary; doing this mentally prevents unconservative answers
Comparison tables
Tied vs. Spiral Column Design Comparison
| Parameter | Tied Column | Spiral Column |
|---|---|---|
| Section shape | Rectangular, polygonal | Always circular |
| Confinement method | Individual tie hoops | Continuous spiral wrap |
| Design reduction factor (φ) | 0.65 | 0.75 |
| Code capacity cap | 0.80 P₀ | 0.85 P₀ |
| Design axial capacity | 0.52 P₀ | 0.6375 P₀ |
| Capacity advantage | Baseline | +23% over tied (same materials) |
| Ductility | Moderate (ties resist Poisson) | Excellent (isotropic confinement) |
| Minimum bars | 4 | 6 |
| Steel ratio limit (ρg) | 0.01 − 0.08 | 0.01 − 0.08 |
| Typical use (Philippines) | Ordinary residential, medium buildings | High-rise, seismic Zone 4, special structures |
| Failure mode below balanced point | Steel yields, ties may spall | Steel yields, spiral confines core |
| Post-failure integrity | Poor (concrete crushes out) | Good (spiral holds core intact) |
Slenderness Limits & Moment Magnification Rules
| Frame Type | k Value | Short-Column Limit (λ = kℓu/r) | Moment Magnification Required? | Typical Example |
|---|---|---|---|---|
| Braced (non-sway) – hinged ends | 0.7 | ≤ 34 − 12(M₁/M₂), max 40 | If λ > limit | Shear-wall supported building |
| Braced (non-sway) – fixed ends | 0.5 | ≤ 34 − 12(M₁/M₂), max 40 | If λ > limit | Moment-resistant frame with lateral bracing |
| Unbraced (sway) – moment frame | 1.0+ | ≤ 22 | Yes, if λ > 22 | High-rise office tower, no shear wall |
| Cantilever | 2.0 | ≤ 22 (very restrictive) | Almost always | Balcony, overhang support column |
Critical φ (Strength Reduction Factor) Values in Column Design
| Failure Mode / Loading | Net Tensile Strain (εt) | φ Value | Interpretation |
|---|---|---|---|
| Compression-controlled (above balanced) | εt ≤ 0.002 | 0.65 (tied), 0.75 (spiral) | Brittle failure; concrete crushes first |
| Transition zone | 0.002 < εt < 0.005 | Linear interpolation | φ = 0.65 + 0.25(εt − 0.002)/0.003 |
| Tension-controlled (below balanced) | εt ≥ 0.005 | 0.90 | Ductile failure; steel yields first |
| Pure flexure (small P or P = 0) | ≥ 0.005 (beam-like) | 0.90 | Treated as beam; large ductility reserve |
Diagrams
Reinforced Concrete Column Design – Concept Map
High-level mindmap showing the five major topics in RC column design and how they interconnect. Use this to organize your thinking before diving into details.
Column Design Decision Tree – Short vs. Slender
Flowchart of the complete column design loop: start with assumed size, check capacity, slenderness, and interaction, then iterate if unsafe. This is the exam workflow.
Failure State Transition Along Interaction Diagram
State diagram showing how the failure mechanism transitions from compression-controlled (brittle) through balanced to tension-controlled (ductile) as you move along the interaction diagram from top to bottom.
Design Axial Capacity Breakdown – Contribution from Concrete vs Steel
Pie chart showing typical split between concrete and steel contributions to axial strength. Most capacity comes from concrete, but steel prevents brittle failure and adds ~30% more capacity. Reminder that net concrete area is used, not gross.
Design Code Evolution for RC Columns (Philippines)
Timeline showing how Philippine column design codes have evolved. NSCP 2015 is the current standard for PRC exams; know that seismic zones require spirals per RA 9389.