House Frame Column Load Calculator: Slab to Footing (Preliminary)
Trace slab, wall and beam loads through a house column grid. Estimate storey axial loads, short-column steel demand and footing area for preliminary planning.
This column load calculator follows gravity loads through a regular house frame: slab to beam to column to footing. It is intended for engineers checking early options, students learning load paths, and people preparing informed questions for their structural engineer. It provides preliminary quantities, not construction dimensions. A licensed structural engineer must design the house.
Start with the number of bays and centre-to-centre column spacing in each direction. Enter the number of elevated slabs supported by the base column, including the roof. For example, a G+1 house may have two supported levels: the first-floor slab and the roof. A slab resting directly on the ground does not load the frame in this model. Every supported level repeats the same geometry, slab, finishes, walls and live load; evaluate unusual roofs, tanks, stairs and transfers separately.
Set slab thickness, concrete unit weight, permanent area loads and imposed live load. The default 2 kN/m² live load illustrates ordinary dwelling rooms under IS 875 Part 2:1987; other occupancies and residential zones can require different loads. Use the project requirements and check against the standard in force. Wall load is entered per metre of every beam line in both directions. Do not enter the same walls again as distributed dead load.
The plan highlights the selected column's tributary area and prints base factored column loads. Select a corner, edge or interior grid intersection to explore its load calculation for building studies. Slab load is assigned one way to X-direction beams using half-distance tributary widths. Y-direction beams carry wall and beam weight. The beam reactions use simple spans; actual continuous frames can distribute reactions differently.
The column screen uses the IS 456:2000 short tied-column axial expression with net concrete area and at least 0.8% longitudinal steel. Trial reinforcement is limited here to 4% for preliminary use. Results include an uncapped algebraic steel demand, an explicit infeasibility warning above the tool's 4% steel limit, and demand divided by conditional axial resistance. Applicability flags examine effective-length ratio and minimum eccentricity; a favourable ratio does not establish safety.
For anyone researching column size for 2 storey house projects, this is a way to compare assumptions, not select a standard column from storey count alone. Footing area uses the unfactored service column load plus an editable allowance for footing and backfill weight, divided by gross allowable soil pressure. The square side rounds upward and is at least the column size.
No lateral, wind, seismic, slenderness or beam-column interaction design is included. Slab and beam reinforcement, deflection, footing thickness, punching shear, settlement, eccentric foundations and boundary restrictions require separate engineering. Length, force, area and pressure fields support the catalog's metric/US switch. The schematic, chart axes and concrete unit-weight field keep explicit SI labels.
How it is calculated
Half-bay tributary factors are 0.5 at a boundary and 1 inside. Their product times the bay area gives each column's slab area. This equilibrium idealization follows the ETH Zurich compendium, attached page 18. Slab load goes one way to X beams; each simple beam transfers half its load to each end. Y beams carry wall and downstand weight only. Summing both directions gives the column loads without duplicating slab load.
Slab self-weight is unit weight times thickness. Beam self-weight uses only depth below the slab. At each level add distributed dead load, assigned beam and wall lengths, full-height column weight, and live load. For n repeated levels: and .
The tied-column screen follows IS 456:2000 cl.39.3: . Solve for steel and enforce . The algebraic demand is retained without a cap, but demand above is explicitly infeasible in this tool and requires a larger section. See IIT Kharagpur Lesson 22, attached pages 4–6. For this equal-depth beam grid, the clear unsupported length is (with consistent units). Minimum eccentricity uses side, with a 20 mm floor, under IS 456 clauses 25.1.3(b) and 25.4. Effective length is . These flags restrict interpretation; no moments or stability are solved.
For gross allowable service soil pressure, . Round the square side upward, at least to the larger column side. Lesson 29, attached pages 5 and 7, supplies independent footing-area benchmarks. No footing strength design is performed.
Assumptions
Regular rectangular grid, uniform bay sizes, identical supported elevated levels, aligned columns and no cantilevers or transfers. The roof repeats the floor loading. Ground-bearing slabs do not load these columns. All grid beams carry the same entered wall line load, including internal lines; change the model elsewhere if the actual wall pattern differs.
The one-way slab transfer is a load-tracing assumption, not a determination of slab action. Continuous-frame reactions may differ. The same total beam depth applies in both directions, so floor height minus beam depth supplies the clear unsupported length for both eccentricity and effective-length screening. Beam intersections and full-height column intersections overlap slightly in the weight estimate, conservatively; full storey height is retained only for column weight. No live-load reduction is applied.
Defaults are a worked planning scenario, not prescribed building dimensions or site soil data. The 2 kN/m² room live load and 25 kN/m³ RC unit weight are illustrated in NIST Structural Design I, attached page 87. Wall load 8.1 kN/m is an explicitly assumed 20 × 0.15 × 2.7 example. The short-column trial is tied RC with 0.8–4% steel; bar count, cover and ties require separate design.
The tributary and equilibrium equations are derived here. Reference cases using zero concrete unit weight isolate prescribed applied loads and are not physical concrete buildings. Diagram and chart labels use SI; numeric inputs and result cards use the catalog unit conversion.
Where it applies
Preliminary sizing only. A licensed structural engineer must design the house. IS 456:2000 and editable room loads referencing IS 875 Part 2:1987 form the stated calculation basis, prepared 26 October 2026; check against the standard in force and local requirements. This is not an ASCE 7 design even if a user enters ASCE occupancy loads.
Conditional axial resistance is meaningful only for short tied columns with eccentricity within the cl.39.3 limit and adequate detailing. The effective-length input and minimum-eccentricity flag are only applicability screens. Steel-area results exceeding 4% of gross area are diagnostic only; they do not specify reinforcement and the trial section must be enlarged. A ratio below 1 is not a safety approval. Edge and corner frame moments require explicit structural analysis.
Excluded: lateral, wind and seismic loads; slenderness and second-order design; axial–moment interaction; slab/beam strength and deflection; reinforcement detailing, robustness and fire; isolated footing bending, punching and one-way shear; settlement calculation, groundwater, uplift, eccentric/boundary footings and soil investigation. Use a site-specific gross allowable pressure that already meets geotechnical bearing and settlement limits, with footing/backfill allowance on the same gross basis.
References
- ETH Zurich, Compendium Structural Design I & II, section 3.4, attached p.18 — tributary areas and published 4 kN / 2 kN per metre examples. https://block.arch.ethz.ch/eq/files/documents/eksjya3zzbiutet2lt8yber6mza89gfx1685609509.pdf
- IIT Kharagpur / NPTEL, Design of Concrete Structures, Lesson 22, Short Axially Loaded Compression Members, pp.4–6 and 8–9; IS 456:2000 clauses 25.4, 26.5.3.1 and 39.3. https://archive.nptel.ac.in/content/storage2/courses/105105104/pdf/m10l22.pdf
- IIT Kharagpur / NPTEL, Lesson 29, Design of Foundations, pp.3–7; service load, gross bearing pressure and footing/backfill allowance. https://archive.nptel.ac.in/content/storage2/courses/105105104/pdf/m11l29.pdf
- NIST, Structural Design I lecture notes, attached pp.87 and 106 (printed pp.83 and 102), residential slab loading and clear unsupported column-height definitions; IS 875 Part 2:1987 and IS 456:2000 cl.25.1.3. https://www.nist.org.in/img/CEN/4TH-SEMESTER/TH-1-STRUCTURAL-DESIGN-I.pdf
Inputs
| Input | Symbol | Unit | Default |
|---|---|---|---|
| Bays in X Regular bays; columns lie at every grid intersection. | n_x | 2 | |
| Bays in Y Up to 4 bays per direction are drawn and tabulated. | n_y | 2 | |
| Column spacing in X Centre-to-centre beam span. The slab load goes to the X-direction beams. | L_x | m | 4 |
| Column spacing in Y Slab tributary width between adjacent X-direction beams. | L_y | m | 4 |
| Supported elevated levels Count slabs carried by the base column, including the roof. Two can represent a G+1 house with a first-floor slab and roof; ground-bearing slabs are excluded. Every level repeats the entered loads. | n_s | 2 | |
| Selected column: X grid index Grid indices start at 0. Select an existing intersection for the detailed results. | j_x | 1 | |
| Selected column: Y grid index The plan highlights this column's tributary area. | j_y | 1 | |
| Floor-to-floor height Full-height column self-weight is included conservatively at every supported level. | H_s | m | 3 |
| Concrete unit weight Normal-weight RC illustration: 25 kN/m³. This field retains SI labels; an explicit US quantity such as 159.14 lbf/ft^3 can also be entered. Zero is a massless-member limit for tracing independently specified applied loads. | g_c | kN/m^3 | 25 |
| Slab thickness Used for slab self-weight, not a slab thickness design. | t_s | mm | 150 |
| Finishes and services dead load Permanent distributed loads in addition to the slab. | q_f | kPa | 1 |
| Other distributed dead load Use only for loads not already counted as beam-line walls. | q_o | kPa | 0 |
| Imposed live load 2 kN/m² illustrates ordinary dwelling rooms under IS 875 Part 2:1987. Edit for occupancy and the standard in force; no live-load reduction. | q_l | kPa | 2 |
| Beam width Same rectangular downstand beam on every grid line. | b_w | mm | 230 |
| Total beam depth Includes slab thickness. Only the downstand is added to slab self-weight. | d_w | mm | 450 |
| Wall dead load on every beam line Same line load in X and Y. Illustration: 20 kN/m³ × 0.15 m × 2.7 m = 8.1 kN/m. Include plaster/openings as appropriate. Zero removes all beam-line walls; do not duplicate these walls in area dead load. | w_w | kN/m | 8.1 |
| Trial column width Uniform trial section throughout the building. No bar layout or ties are designed. | b_c | mm | 400 |
| Trial column depth A capacity screen only; frame moments and lateral design may require a larger section. | d_c | mm | 400 |
| Concrete characteristic cube strength IS 456:2000 material definition, not cylinder strength f′c. | f_ck | MPa | 25 |
| Reinforcement characteristic strength The axial expression uses 0.67 fy. | f_y | MPa | 500 |
| Trial longitudinal steel fraction 0.01 = 1%; minimum 0.008 = 0.8%. This preliminary tool limits trial steel to 4% to avoid congested arrangements. | r_s | 0.01 | |
| Effective length / clear unsupported length User-supplied restraint factor: effective length = this factor × clear unsupported length (floor height minus beam depth). Used only for the short-column flag; stability is not designed. | k_e | 0.8 | |
| Gross allowable soil bearing pressure Site-specific allowable service pressure including settlement restrictions. Obtain from a geotechnical engineer; do not enter an ultimate bearing resistance or a net value. | q_a | kPa | 150 |
| Footing and backfill load / column load 0.10 means an estimated 10% extra service load. Replace after footing thickness and cover soil are known. | r_f | 0.1 | |
| Footing side rounding increment Each square footing side is rounded upward. No thickness, reinforcement or shear design. | s_f | mm | 50 |
Results
With the default inputs above, the calc gives:
| Result | Value |
|---|---|
| Selected base service axial load | 397.2 kN |
| Selected base factored axial load | 595.8 kN |
| Largest base factored column load | 595.8 kN |
| Trial axial resistance — conditional | 2,120 kN |
| Selected demand / conditional resistance | 0.281 |
| Selected steel range — axial screen only | Demand within 0.8–4% range |
| Algebraic steel demand — invalid above 4% | 1,280 mm² |
| Required steel fraction — limit 0.04 | 0.008 |
| Trial steel area provided | 1,600 mm² |
| Selected bearing area required | 2.913 m² |
| Selected rounded square footing side | 1.75 m |
| Selected gross service bearing pressure | 142.7 kPa |
Checked against sources
Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).
ETH published tributary column example
Source: ETH Zurich Structural Design I & II compendium, section 3.4, attached p.18. Published 2 m by 2 m tributary area under 1 kN/m² gives 4 kN. The case isolates that applied load with massless members and no walls; it does not validate a whole house.
Inputs: Concrete unit weight = 0 kN/m³; Finishes and services dead load = 0 kPa; Wall dead load on every beam line = 0 kN/m; Supported elevated levels = 1; Column spacing in X = 2 m; Column spacing in Y = 2 m; Imposed live load = 1 kPa; the others as above.
| Result | Source | This calc |
|---|---|---|
| Selected tributary area | 4 m² | 4 m² |
| Selected base service axial load | 4 kN | 4 kN |
ETH published tributary beam example
Source: ETH compendium, section 3.4, attached p.18. Published 8 m² beam strip over 4 m length under 1 kN/m² gives 2 kN/m. Massless beams, columns and slab isolate the applied surface load.
Inputs: Concrete unit weight = 0 kN/m³; Finishes and services dead load = 0 kPa; Wall dead load on every beam line = 0 kN/m; Supported elevated levels = 1; Column spacing in Y = 2 m; Imposed live load = 1 kPa; the others as above.
| Result | Source | This calc |
|---|---|---|
| Service load on an interior X beam | 2 kN/m | 2 kN/m |
NIST residential slab published loading
Source: NIST Structural Design I, attached p.87, printed p.83, slab S2 example: 120 mm RC at 25 kN/m³, finishes 1, live 2 kN/m², service 6 and factored 9 kN/m². Only the area-loading part is compared.
Inputs: Slab thickness = 120 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Slab self-weight | 3 kPa | 3 kPa |
| Total distributed dead load | 4 kPa | 4 kPa |
| Service distributed slab load | 6 kPa | 6 kPa |
| Factored distributed slab load | 9 kPa | 9 kPa |
IIT Kharagpur required column steel benchmark
Source: IIT Kharagpur Lesson 22, attached pp.8–9, Problem 1. A 400 × 600 mm M25/Fe415 column under 2000 kN service needs 2238.39 mm² steel. The massless 100 m² load patch is a harness for the published column demand, not its building geometry. The published eccentricity calculation substitutes effective length 2600 mm for unsupported length 4000 mm. Clause 25.4 uses unsupported length: the tool correctly obtains 21.33 mm for the 400 mm direction, exceeding 0.05b=20 mm, and flags axial-only applicability. The steel-equation benchmark still agrees; it does not validate that example's applicability conclusion.
Inputs: Concrete unit weight = 0 kN/m³; Finishes and services dead load = 0 kPa; Wall dead load on every beam line = 0 kN/m; Supported elevated levels = 1; Column spacing in X = 10 m; Column spacing in Y = 10 m; Imposed live load = 20 kPa; Floor-to-floor height = 4.45 m; Trial column depth = 600 mm; Reinforcement characteristic strength = 415 MPa; Effective length / clear unsupported length = 0.65; the others as above.
| Result | Source | This calc |
|---|---|---|
| Selected base service axial load | 2,000 kN | 2,000 kN |
| Selected base factored axial load | 3,000 kN | 3,000 kN |
| Algebraic steel demand — invalid above 4% | 2,238 mm² | 2,238 mm² |
IIT 400 kN footing with 15% allowance
Source: IIT Kharagpur Lesson 29, attached pp.3–5, Problem 1: service load 400 kN, gross allowable pressure 300 kN/m², 15% allowance, 1.533 m² area, 1.25 m provided side and 294.4 kPa pressure. The text calls the allowance a percentage of Pu but its arithmetic uses service load; the tool follows the correct service basis. Massless load patch reproduces the specified column force only.
Inputs: Concrete unit weight = 0 kN/m³; Finishes and services dead load = 0 kPa; Wall dead load on every beam line = 0 kN/m; Supported elevated levels = 1; Imposed live load = 25 kPa; Gross allowable soil bearing pressure = 300 kPa; Footing and backfill load / column load = 0.15; the others as above.
| Result | Source | This calc |
|---|---|---|
| Selected base service axial load | 400 kN | 400 kN |
| Selected bearing area required | 1.533 m² | 1.533 m² |
| Selected rounded square footing side | 1.25 m | 1.25 m |
| Selected gross service bearing pressure | 294.4 kPa | 294.4 kPa |
IIT 1500 kN footing with 10% allowance
Source: IIT Kharagpur Lesson 29, attached pp.6–7, Problem 2. Published 1500 kN service load and 250 kN/m² gross allowable pressure with 10% footing/backfill allowance give 6.6 m²; provided square side 2.6 m. Massless load patch isolates the prescribed column force; thickness and reinforcement are not compared.
Inputs: Concrete unit weight = 0 kN/m³; Finishes and services dead load = 0 kPa; Wall dead load on every beam line = 0 kN/m; Supported elevated levels = 1; Column spacing in X = 10 m; Column spacing in Y = 10 m; Imposed live load = 15 kPa; Gross allowable soil bearing pressure = 250 kPa; the others as above.
| Result | Source | This calc |
|---|---|---|
| Selected base service axial load | 1,500 kN | 1,500 kN |
| Selected bearing area required | 6.6 m² | 6.6 m² |
| Selected rounded square footing side | 2.6 m | 2.6 m |
Responses