Every structural element in a building is sized from the loads it must carry. Columns, beams, walls, and slabs each receive loads from the elements above them, and the calculation method traces those loads down the building until they reach the foundation. A column is a vertical compression member that transfers the load of the superstructure to the foundation safely. Beams resist bending and carry vertical gravitational forces, and in some positions horizontal loads as well. Walls enclose the building and, when load bearing, carry the floors and roof above. Slabs collect the loads of occupants, furniture, and equipment over their area. Getting the numbers right matters because every downstream member is sized from them. Once the member sizes are known, the concrete calculator for slab, beam, column, and footings is a useful check on the volume side of the design.
The load acting on any member is the design load: the sum of the dead and live loads that reach it, factored for safety. This article walks through the calculation for each member type, starting with the definitions and ending with worked examples.
The Members and How They Work Together
A building’s gravity load path runs from the slab to the beams, from the beams to the columns and walls, and from the columns and walls to the footings. Each member hands its load to the member below it, and the accumulated load at any level is the sum of everything above.
Columns
A column is defined as a vertical compression member that is mainly subjected to axial loads and whose effective length exceeds three times its least lateral dimension. The compression member whose effective length is less than three times its least lateral dimension is called a pedestal. A compression member that is inclined or horizontal and is subjected to axial loads is called a strut, and struts are used in trusses. Columns, struts, and pedestals are the compression members used in buildings, bridges, supporting systems of tanks, and factories.
Beams, Walls, and Slabs
A beam is a structural element that resists bending. It carries vertical gravitational forces and also pulls the horizontal loads acting on it. The beam that sits on top of a wall is called a wall plate or sill plate, and it transmits the load to girders, columns, or walls below. In the early centuries timbers were the preferred beam material; today beams are made of aluminum, steel, reinforced concrete, and other materials that bear the shear forces and bending moments.
The share of load each member receives depends on geometry. For floor systems the slab is divided into tributary areas, one for each supporting beam or column line, and the load within each area is assigned to that support. The tributary area method in column load transfer is the standard way to distribute floor loads before any member is sized.
Dead Load, Live Load, and Design Load
Load calculations on column, beam, wall, and slab use the same basic vocabulary: dead load, live load, and the factored design load. Dead load is the self-weight of the structure and everything permanently attached to it. Live load is the movable and temporary load from people, furniture, vehicles, and stored goods. The design load is the combination of the two, factored for safety.
Dead Load
Dead load is computed from material densities and member dimensions. A reinforced concrete slab 150 mm thick weighs about 3.6 kN per square meter, and a 230 mm brick wall with plaster weighs roughly 4.5 to 5.0 kN per square meter. The engineer sums the self-weight of every element in the load path, using typical unit weights such as these:
| Material | Typical unit weight |
|---|---|
| Reinforced concrete | 24 to 25 kN/m3 |
| Brick masonry | 18 to 20 kN/m3 |
| Stone masonry | 20 to 24 kN/m3 |
| Timber | 6 to 8 kN/m3 |
| Steel | 78.5 kN/m3 |
Live Load
Live loads are set by codes based on the use of the space. A residential floor is commonly designed for 1.5 to 2.0 kN per square meter, an office for 2.5 to 3.0, and a storage area for 5.0 or more. Live loads can be partial, concentrated, or moving, and the code dictates the arrangement that produces the worst effect on the member.
The calculation sequence used in practice follows a standard order: collect the tributary area, compute the dead load, add the code live load, and factor the sum. The worked examples in the load calculation reference on column, beam, wall, and slab show each step with numbers, which makes the procedure easier to follow than a formula list.
Load Calculation on Column
A column carries the tributary loads from the slab and beams above it, plus the self-weight of the column itself, plus the weight of any wall that bears on it. The axial load at the column base is the total of all these contributions for every floor above.
The Column Load Equation
For a column supporting a floor system, the load equals the tributary area times the floor load, plus beam self-weight, plus wall weight, plus column self-weight. Each term is a dead or live load component, and the components are factored before the column is designed.
Factored vs Unfactored Loads
The unfactored sum is called the service load. The factored design load applies load factors from the code, commonly 1.2 times the dead load plus 1.6 times the live load, which covers the uncertainty in the loads and the variability of the materials. Columns and their footings are designed for the factored load, while settlement and deflection checks use the service load.
Worked Example
- Take a column with a tributary area of 4 m by 5 m, or 20 square meters per floor
- Assume a total floor load of 10 kN per square meter, including slab, finishes, partitions, and live load
- The slab and beam load reaching the column is 20 times 10, or 200 kN per floor
- Add the self-weight of the beam, say 15 kN per floor, for 215 kN per floor
- For a three story building, the accumulated load is about 645 kN before the column self-weight
- Add the column self-weight and apply the code load factors to get the design axial load
Vertical Members and Their Supports
The same calculation logic extends below the column into the foundation. When columns are supported on piles, the pile load capacity calculation for single piles and group piles determines how many piles are needed, and the pile layout is checked for both capacity and settlement.
Load Calculation on Beam, Wall, and Slab
Each horizontal member follows the same logic with a different geometry. The slab collects load over its area, the beam collects load over its tributary width, and the wall collects load over its tributary height.
Slab Load
A slab carries its self-weight, floor finishes, and live load over its full area. The design load per square meter is the sum of the dead and live components, and the slab is then designed for the bending moments and shear that the load produces.
Beam Load
A beam receives the load from the slab area on either side of it, up to the mid span of the adjacent slab panels. The result is a uniformly distributed load in kilonewtons per meter along the beam, plus any point loads from secondary beams or walls bearing on the beam.
Wall Load
A load bearing wall carries the loads from the floor or roof above it, distributed along its length, plus its own weight. The load per meter of wall is the sum of the supported loads divided by the wall length, and the wall is checked for the resulting axial stress.
Load accounting is not limited to the structure itself. Building services follow the same discipline: an HVAC load calculation for commercial construction works through the heat gains and losses of the space and sizes the equipment, just as the structural load calculation sizes the members. Both start from the same principle of listing every load, adding it up, and applying the appropriate factors.
From Member Loads to Foundation Design
Once the member loads are known, the design moves down the load path: columns are designed for axial load and buckling, beams for bending and shear, and footings for soil bearing pressure. The member sizes must satisfy the code requirements for strength and serviceability at every level.
Checking the Frame
For steel buildings the frame is checked using the methods of structural steel design, covering beam design, column buckling, connections, and composite construction. Buckling checks matter for columns because a slender compression member can fail at a fraction of its crushing load.
The Load Path to the Soil
The foundation spreads the column and wall loads over the soil. The bearing pressure under the footing must stay below the allowable soil bearing capacity, and the settlement must stay within acceptable limits. If the soil is weak, the footing grows larger, or the load is transferred to piles or a raft.
Putting Load Calculations to Work
Load calculation is not an academic exercise. The numbers produced at the start of the design control the column sizes, beam depths, wall thicknesses, and footing dimensions used on site, and they reappear whenever the building is modified.
Common Uses
- Sizing new members during design
- Checking existing buildings before adding floors or equipment
- Evaluating walls before openings are cut
- Verifying that a foundation can accept a new load
When Existing Buildings Are Modified
When a building is changed, the existing structure must be rechecked for the new loads. Seismic retrofitting and earth retention projects use the evaluation procedures of ASCE 41 to assess existing columns and walls, strengthen them where needed, and design retaining structures, a process that starts with the same load calculation on every member.