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Civil & Structural Engineering Ag req · sizing

RCC Column Preliminary Sizing Calculator

28 September 2026 11 min read

Conservative gross area and square size from factored load for early column layouts.

Suggested size: 450 mm sq; rounded to 50 mm

Live statistics

Ag required

171429 mm2

Square side

414 mm

Use

450 mm sq

Unit system

Factored load Pu(kN) Help

Factored axial demand.

Concrete fc(MPa) Help

MPa

Cylinder strength.

Results update live as you type

How you compare — standard sections

Section	Depth (mm)	Mass (kg/m)	A (cm²)	Iₓ (×10⁶ mm⁴)	Sₓ (×10³ mm³)
UB 305×165×40 · Steel I-beam	304	40.3	51.3	85	560
UB 457×191×67 · Steel I-beam	454	67.1	85.5	294	1290
UC 254×254×73 · Steel column	254	73.1	93.1	114	895
RC 300×500 (C30) · Concrete beam	500	375	1500	3125	12500
Glulam 140×450 · Timber beam	450	29	630	1063	4725
SHS 200×200×8 · Hollow section	200	47.4	60.4	36.9	369

Indicative values for scheme design only. Always verify against the manufacturer / code tables (AISC Steel Manual, SCI Blue Book, ACI detailing) before ordering steel or pouring concrete.

Plans & details

Detail

Column section detail

Cover, ties and bar layout per ACI 318. Extend bars past the joint plus development length.

Path

Load path sketch

Slab to beam to column to footing. Verify tributary areas before issuing numbers.

Check

Site verification

Confirm concrete strength, cover and compaction against drawings and test records.

Typical details for scheme design. Replace placeholders with project drawings (1200×630 JPG or SVG line work in /public/plans/civil/). Do not scale from web images — use figured dimensions.

Design verification checklist

Work through before issuing results — 1/6 verified (17%).

Results

Normal

Required gross area

171429mm2

Pu over a conservative 0.35 fc allowance.

Exact square side

414mm

Square root of required area.

Suggested column size

450.0mm

Rounded up to the next 50 mm for layout.

Visualizations

Results Overview

171,429mm2Required gross area

414mm2Exact square side

450mm2Suggested column size

Formula

A deliberately conservative stress allowance converts factored load into a gross area, then into an exact square side and a buildable size rounded up to 50 mm.

Ag,req = Pu x 1000 / (0.35 fc) | side = sqrt(Ag) | suggested = round up to 50 mm

Alternative Form

Refine later with actual rho, moments and slenderness

Variables

Symbol	Name	Unit	Description
Ag,req	Required gross area	mm2	Conservative concrete area for Pu.
side	Exact square side	mm	Root of Ag,req.
sugg	Suggested size	mm	Buildable square rounded up.

Explanation

Conservative allowable stress gives area; square root plus 50 mm rounding gives the layout size.

Derivation

Invert an allowable-stress style relation Pu = 0.35 fc Ag for area, take the square root for a square section, and round up for placing tolerance.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Enter factored Pu and concrete fc

Result: Demand fixed

Step 2

Read required gross area

Result: Area issued

Step 3

Read suggested square size

Result: Layout size issued

Final Answer

171429

Worked Examples

See how the calculator works with different scenarios.

Scenario

Early grid layout on 25 MPa concrete.

Inputs

Pu:1500

fc:25

Calculation

Ag is 1500000 / 8.75 = 171429 mm2. Side is sqrt(171429) = 414 mm, so round up to a 450 mm square.

Result

Use 450 mm square

Interpretation

A 450 by 450 column fits the grid; verify with steel ratio and moments next.

Understanding Your Result

Your Result: Required gross area = 171429 mm2 · Exact square side = 414 mm · Suggested column size = 450.0 mm

Typical range: Offices often land on 300 to 600 mm squares.

What This Means

Smallest square that plausibly carries Pu at scheme stage.

Why It Matters

Grid and architecture lock early; a fast conservative size keeps floors coordinated.

Professional Interpretation

Issue the suggested size with Pu and fc stated, then replace it with a full interaction check.

Recommendations

•Check slenderness before trusting short-column capacity
•Keep service and factored (1.2D + 1.6L) columns separate
•Verify one line by hand per schedule

Learn — structural behaviour, deeply

One load in, one sensible square out.

1 · The two equations that run every site

ΣF_y = 0

Vertical balance

Upward reactions must equal total downward load. Missing 1 kN here means a 1 kN shear error everywhere downstream.

ΣM = 0

Moment balance

Moments about ANY point must cancel. Take moments about one support to eliminate it and solve the other directly.

ΣF_x = 0

Horizontal balance

Zero for vertical-only loading — but the pin still needs checking once wind, soil or inclined loads appear.

Worked derivation (simply supported, point load): ΣMleft = 0 ⇒ Rb·L − P·a = 0 ⇒ Rb = P·a/L, then ΣFy = 0 ⇒ Ra = P − Rb = P·(L−a)/L. UDL adds w·L/2 per side acting at midspan. That is the entire calculation — everything else is bookkeeping.

2 · Support types — what each one can (and cannot) do

Support	Reactions	Allows	Watch out
Roller	1 (vertical)	Horizontal slide + rotation	Provides NO lateral restraint — pair with a pin or bracing.
Pin / hinge	2 (vertical + horizontal)	Rotation only	Moment released here — detail the hinge, never weld it rigid by accident.
Fixed / clamped	3 (+ moment)	Nothing (fully restrained)	Attracts large moments; settlement or temperature causes locked-in stress.
Propped cantilever	3 (indeterminate ×1)	Rotation at prop	Needs compatibility (deflection = 0 at prop) — equilibrium alone is not enough.
Continuous (3+ supports)	4+ (indeterminate)	Rotation over interior piers	Solve by superposition / moment distribution / software; reactions shift with stiffness.

3 · Factor-impact table — what moves your reactions most

Factor	Typical impact	Why
Load position (a/L)	Linear, dominant	Moving P toward a support shifts ~100% of P onto it. Ra = P·(L−a)/L — position matters more than span.
UDL intensity (w)	∝ w·L total	Each extra 1 kN/m on a 6 m beam adds 3 kN per reaction. Self-weight alone is often 1–5 kN/m on concrete.
Span length (L)	∝ L for UDL	Doubling L doubles UDL reactions and quadruples UDL moment (wL²/8). Keep spans tight where possible.
Overhang length (c)	∝ c/L uplift	Uplift at the far support = P·c/L. A 2 m overhang with 10 kN on a 5 m span pulls down 4 kN — needs hold-down.
Fixity (pinned → fixed)	Redistributes ~10–30%	Fixed ends attract moment and shed midspan moment. Never assume fixity you have not detailed.
Support settlement (Δ)	0 (det.) / large (indet.)	Determinate beams just rotate; continuous/fixed beams develop locked-in moments ≈ 3EIΔ/L².
Dynamic / impact	+10–100%	Static reactions must be amplified for cranes, machinery, footfall (see ASCE 7 Ch. 4, AISC DG11).
Load combination	× 1.2–1.6 (LRFD)	1.2D + 1.6L + 0.5(Lr/S/R) governs most beams. Reactions for strength ≠ reactions for service checks.

4 · Code provisions you must cite on drawings

ASCE 7 load combinations (LRFD): 1.4D · 1.2D + 1.6L + 0.5(Lr/S/R) · 1.2D + 1.0W + 1.0L … Strength reactions use factored loads; bearing/deflection checks use service (unfactored) loads.
ACI 318 (concrete): strength-reduction ϕ = 0.65–0.90; development/lap lengths Ch. 25; one-way shear + punching Ch. 22. Reactions feed directly into Vu ≤ ϕVn.
AISC 360 (steel): Ch. F/G/H for moment/shear/combined; bearing at supports per J7–J8; bracing per App. 6. Connection must develop the computed reaction — a beam is only as strong as its seat.
Eurocode basis (EN 1990): ULS 1.35G + 1.5Q; SLS G + Q (characteristic). National annexes adjust factors — confirm the project annex.
Serviceability (all codes): live-load deflection ≈ L/360 floors, L/240 roofs; total ≈ L/240. Vibration: AISC DG11 / SCI P354 for rhythmic or office floors.

5 · Pro workflow (5 minutes per beam)

Sketch the free-body diagram: every load incl. self-weight, every support, dimensions.
Solve ΣM then ΣF — write both lines on the calc sheet so a checker can follow.
Verify: re-take moments about the OTHER support; residual must be ≈ 0.
Draw shear then moment (reactions are the SFD starting values).
Size the support: bearing stress, padstone, bolt/weld group, foundation pressure.
File: keep the input → reaction → SFD/BMD → support chain on one page.

6 · Field traps (where reactions go wrong)

• Forgetting self-weight: a 300×600 concrete beam weighs 4.5 kN/m — on 6 m that is 13.5 kN per support.
• Assuming fixity: a “fixed” sketch with two bolts is a pin. Model what you detail.
• Ignoring uplift: overhang + wind can reverse a bearing — light roofs lift off.
• Mixing factored/service: never compare a factored reaction against an allowable soil pressure.
• Point load at the wrong station: 0.5 m error on a 10 kN load swings reactions by P·Δa/L.

7 · The 3-check rule (sign-off standard)

Math check: ΣFy and ΣM both close to zero with project units printed.
Sanity check: reactions sum to total load; heavier side sits under heavier load; UDL symmetry gives Ra ≈ Rb.
Load-path check: every reaction lands on something sized for it — beam → seat → column → footing → soil, no floating numbers.

Practical Tips

•Split dead vs live early — factoring depends on it
•Include self-weight; concrete often dominates
•Report service values to 1 decimal for bearings and footings

Common Mistakes

Service load checked against factored capacity

Keep a service column (settlement, soil, deflection) and a factored column (strength) side by side.

Self-weight omitted

Add member weight into the total first.

Wrong units in one term

Convert everything to the page unit system before combining terms.

Assumptions

This calculator makes the following assumptions to provide estimates:

Static gravity loading: No impact, vibration or seismic amplification unless the page applies one.

Nominal material properties: Code-grade materials per project data; confirm lightweight or high-strength cases.

Scheme-level accuracy: Closed-form code clauses for preliminary and check calculations.

Limitations

Be aware of these limitations when using this calculator:

Verify supports and pattern: Pattern loading, continuity and support settlement need their own runs.

Confirm local code values: Loads, factors and minimums vary by jurisdiction.

Frequently Asked Questions

Answers to common questions about this calculator.

Why 0.35 fc?

It is a conservative scheme allowance covering steel contribution, minimum eccentricity and strength reduction in one number.

What about moments?

This sizes for axial load only. Rectangularise or enlarge once beams frame in with moment.

Why round to 50 mm?

Formwork and placing favour 50 mm modules; rounding up keeps the check conservative.

Is this a final design?

No, it is a preliminary size per simplified ACI 318 ideas. A licensed engineer must confirm final design.

How do I find reactions for a simply supported beam?

Take moments about the left support: Rb = (P·a + w·L·L/2) / L, then Ra = P + w·L − Rb. Always re-check by taking moments about the right support — the residual must be ≈ 0.

What does a negative (downward) reaction mean?

The support must pull DOWN instead of pushing up — net uplift from overhangs, pattern loading or wind. Provide a hold-down strap, anchor or ballast; a gravity-only bearing will lift off.

Do I include the beam self-weight?

Yes, always. A 300×600 mm concrete beam weighs ~4.5 kN/m — on a 6 m span that adds ~13.5 kN per support. Bundle it into the UDL before solving.

Service vs factored loads — which do I report?

Report BOTH in separate columns: service (unfactored D+L) for deflection, bearing, settlement and soil checks; factored LRFD (1.2D + 1.6L) for member strength. Never compare a factored reaction with an allowable soil pressure.

What is the difference between a UDL and a UVL?

A UDL (uniformly distributed load) is constant intensity over a length (kN/m). A UVL (uniformly varying / triangular) runs zero-to-max — e.g. soil or hydrostatic pressure. They integrate differently, so use the matching calculator.

How do I turn a floor area load into a beam line load?

Multiply the area load (kN/m²) by the tributary width (m) draining to the beam: line load = area load × tributary width. Add the beam self-weight, partitions and finishes first.

What is tributary area?

The floor/roof area whose load flows to one member — bounded by halfway lines to adjacent members. Tributary area × area load = the point/line load that member must carry.

Which load combination usually governs a beam?

For strength: 1.2D + 1.6L (+ 0.5 for roof live/snow/rain) per ASCE 7 LRFD. Service D+L governs deflection and bearings; 0.9D + 1.0W governs uplift and overturning.

LRFD vs ASD — does it change the reactions?

No — equilibrium is the same. The design PHILOSOPHY differs: LRFD factors loads up (1.2D+1.6L) against factored resistance (ϕRn); ASD keeps service loads against allowable stresses (Rn/Ω). Keep the two systems in separate columns.

Pin, roller or fixed — how do I choose the support model?

Model what you DETAIL. Masonry/steel seats and two-bolt end plates are pins (moment released); moment frames, welded rigid joints and well-anchored cantilevers earn fixity. When in doubt, the pinned assumption is conservative for midspan moment but NOT for uplift.

What deflection limits apply to beams?

Typical code limits: live-load deflection L/360 for floors (L/240 roofs), total-load L/240, cantilevers 2L/360-ish per IBC Table 1604.3. Always check under SERVICE loads with the correct (cracked, long-term) stiffness.

How do I convert kN ↔ kips and m ↔ ft?

1 kN = 0.2248 kips (1 kip = 4.448 kN); 1 m = 3.2808 ft. Moments: 1 kN·m = 0.7376 kip·ft. Every calculator on this site has an SI/Imperial toggle that converts all displayed values.

Shear vs bending moment — which sizes what?

Shear sizes stirrups/webs and connections (V ≤ ϕVn); bending moment sizes flexural steel and the section (M ≤ ϕMn via section modulus S: stress = M/S). Deflection is governed by stiffness EI, a third independent check.

Where does the maximum moment occur?

Where shear crosses zero: under a midspan point load, or at x = R/w under UDL (span moment = R·x − w·x²/2). On continuous beams also check the hogging peaks OVER interior supports — they often govern.

What is section modulus and how do I use it?

S = I/c (mm³): the geometric bending efficiency of a section. Bending stress = M/S; required S = factored moment / allowable (or design) stress. Compare against the standard-section table on each page.

How do I quickly check a steel beam?

Three checks per AISC 360: bending (Ch. F incl. lateral-torsional buckling over the unbraced length), shear (Ch. G), and deflection (L/360). Then verify the connection develops the end reaction.

How do I quickly check a concrete beam?

Flexure per ACI 318: ϕMn = ϕ·As·fy·(d − a/2) with ϕ = 0.9 (tension-controlled); one-way shear Vc + Vs (Ch. 22); deflection via minimum thickness or direct computation with cracked stiffness and long-term multiplier.

What is development length and why does it matter?

The embedment needed for a bar to reach yield (ld, ACI 318 Ch. 25). A perfectly computed moment capacity is worthless if the bar pulls out — extend bars past inflection points and hook or develop them at supports.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

Reaction: Force (or moment) a support exerts on a member to maintain static equilibrium (ΣF = 0, ΣM = 0).
Simply supported: Beam on one pin + one roller. Resists vertical load; allows rotation and (at roller) horizontal movement.
Fixed support: Clamped end resisting force AND moment; prevents rotation. Used in cantilevers and fixed frames.
UDL / UVL: Uniformly distributed load (constant kN/m) vs. uniformly varying load (triangular, zero-to-max).
Tributary area: Floor/roof area whose load drains to one member. Line load = area load × tributary width.
Factored load: Service load × LRFD load factor (e.g. 1.2D + 1.6L) for strength design per ASCE 7.
Serviceability: Deflection, cracking and vibration limits under day-to-day (unfactored) loads.
Uplift: Net downward-hold requirement: a negative (downward-pulling) reaction, common on overhangs.

Authoritative References

Trusted sources and standards referenced by this calculator.

ACI 318 Code & Commentary (American Concrete Institute) AISC Steel Construction Manual ASCE 7 Hazard Tool — design loads Eurocodes (EN 1990–1999) — Basis of Structural Design Hibbeler — Structural Analysis (textbook companion) NIST — Wind & Seismic design resources

Applicable Standards

ACI 318 — Building Code Requirements for Structural ConcreteAISC 360 — Specification for Structural Steel BuildingsASCE 7 — Minimum Design Loads and Associated CriteriaEurocode 2 (EN 1992) — Design of Concrete StructuresEurocode 3 (EN 1993) — Design of Steel StructuresIBC — International Building Code (structural chapters 16–23)

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Last Updated:

2026-09-28

Version:

2.0.0

References:

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Free to use for educational and professional purposes.