Load Calculation Calculator

About Load Calculation

This load calculation calculator determines structural loads acting on beams, columns, and slabs. It sequentially calculates the self-weight of structural elements, loads from layers and partitions, includes snow and imposed loads, applies design factors, and determines the resulting load on the selected structural element.

For a slab, the result is expressed as an area load in kg/m² and kN/m². For a beam, area loads are converted into line loads in kg/m and kN/m, and the total load on the beam is also calculated. For a column, the total design load is determined in kg and kN.

Guidelines and recommendations

Design basis

Permanent and variable actions. The load combination logic follows the principles of EN 1990 “Eurocode — Basis of structural design”. Self-weight, material densities, and imposed loads are related to EN 1991-1-1 “Eurocode 1: Actions on structures — Part 1-1: General actions — Densities, self-weight, imposed loads for buildings”, while snow loads are based on EN 1991-1-3 “Eurocode 1: Actions on structures — Part 1-3: General actions — Snow loads”.

Design factors. The calculator uses γ_G = 1.35 for all permanent loads. The leading variable load is multiplied by γ_Q = 1.50. When snow load and imposed load act simultaneously, the accompanying action is additionally reduced by the combination factor ψ₀.

Permanent loads

General principle. The self-weight of the slab, beam, column, secondary beams, structural layers, and partitions is treated as a permanent load. The characteristic mass of each component is first calculated and then multiplied by 1.35.

Gd = 1.35 · G

Solid slab. For a solid reinforced concrete slab, a density of 2500 kg/m³ is used. For a slab thickness h in mm, the characteristic self-weight per square metre is calculated as:

qslab = (h / 1000) · 2500

The result is obtained in kg/m². For example, a 200 mm thick slab has a characteristic mass of 500 kg/m²; after applying the factor 1.35, the design component is 675 kg/m².

Hollow-core and ribbed slabs. For these structures, the mass is entered directly in kg/m² because it depends on the geometry of the voids and ribs. For preliminary estimates, values of about 250–450 kg/m² are often used for reinforced concrete hollow-core slabs and 150–400 kg/m² for ribbed slabs. If manufacturer data are available, the actual mass per square metre should be used.

Loads from structural layers

Material with a known density. If a layer has a density ρ in kg/m³, its area mass is calculated from the thickness t in mm:

qlayer = (t / 1000) · ρ

For example, a 50 mm layer with a density of 1600 kg/m³ produces a characteristic load of 80 kg/m². After multiplication by 1.35, the design load is 108 kg/m².

Material with a predefined area mass. For materials whose load is already specified in the calculator in kg/m², this value is used directly. The design load of each permanent layer is then obtained by multiplying it by 1.35.

Partition load

Total mass. The mass of partitions is calculated from their total length L_p, thickness t_p, height h_p, and material density ρ. Dimensions entered in millimetres are first converted to metres:

Mpart = (Lp / 1000) · (tp / 1000) · (hp / 1000) · ρ

Distribution over the area. The resulting mass is distributed over the considered area A, so the equivalent area load is:

qpart = Mpart / A

For a slab, the slab area is used. In beam and column calculations, the partitions are distributed over the corresponding tributary area. The resulting value is treated as a permanent load and multiplied by 1.35.

Snow and imposed loads

Input values. Snow and imposed loads are entered as characteristic values before applying γ_Q. Values can be entered in kg/m² or kN/m². The conversion uses 1 kg = 0.00980665 kN.

Practical reference values. For a preliminary estimate of snow load in a temperate climate, approximately 100 kg/m², or 0.98 kN/m², can be used as a reference, but the actual value should be determined according to EN 1991-1-3 and the applicable National Annex. For imposed loads, commonly used values are about 150–200 kg/m² for residential areas, 200–300 kg/m² for offices, and 400–500 kg/m² for retail areas; the exact value depends on the occupancy category according to EN 1991-1-1 and the National Annex.

Single variable load. If only snow load or only imposed load is specified, that load is treated as the leading variable action and is applied in full with a factor of 1.50. The ψ₀ factor does not reduce the load in this case.

Combination of snow and imposed loads

Two load combinations. If both snow load S and imposed load Q are greater than zero, the calculator evaluates two combinations. In the first, the imposed load is leading and the snow load is accompanying:

EQ = 1.35 · G + 1.50 · Q + 1.50 · ψ0,S · S

In the second combination, the snow load is leading. For the accompanying imposed load, the calculator automatically uses ψ_0,Q = 0.70:

ES = 1.35 · G + 1.50 · S + 1.50 · 0.70 · Q

Selection of the design value. The combination producing the greater total design load is used as the final result:

Ed = max(EQ, ES)

Snow combination factor. By default, ψ_0,S = 0.50 is used. This value can be changed from 0 to 1 according to the applicable National Annex. With ψ_0,S = 0.50, the effective design factor for accompanying snow is 1.50 · 0.50 = 0.75.

Imposed load combination factor. When the imposed load is accompanying, its effective factor is 1.50 · 0.70 = 1.05. When it is the leading action, the full factor 1.50 is used.

Design factor shown in the results. For variable loads, the results table shows the factor actually applied after considering the load combination. Therefore, the same imposed load may have a factor of 1.50 when it is leading or 1.05 when it is accompanying; for snow, the factor is either 1.50 or 1.50 · ψ0,S.

Slab load calculation

Permanent component. The self-weight of the slab is combined with the loads from all selected layers and partitions. Each permanent component is multiplied by 1.35, after which the governing combination of snow and imposed loads is added.

qd = 1.35 · (qslab + Σqlayer + qpart) + Qd,var

The result is the design area load in kg/m² and kN/m².

Beam load calculation

Tributary width. An area load q in kg/m² is converted into a line load using the beam spacing B entered in millimetres:

w = q · B / 1000

For example, with B = 900 mm, each metre of the beam carries the load from a 0.9 m wide strip. The total load from each line-load component is obtained by multiplying it by the beam length L:

P = w · L / 1000

Beam self-weight. For a rectangular section, the mass of one metre of beam is calculated from the width b, height h in mm, and density ρ in kg/m³:

mbeam = b · h · ρ / 106

For standard steel I-sections, channels, hollow sections, and angles, the tabulated mass of the selected profile in kg/m is used. Beam self-weight is multiplied by 1.35.

Secondary beams. Their number is calculated from the main beam length L and the specified spacing L₁, rounded upward:

n = ceil(L / L1)

The mass of each secondary beam is calculated from its cross-section or tabulated profile mass and its length, which is equal to the width of the tributary area. The total mass of all secondary beams is distributed along the main beam and treated as a permanent load with a factor of 1.35.

Column load calculation

Transfer of area loads. Loads from structural layers, partitions, snow, and imposed load are converted into a total load over the rectangular tributary area L · B:

P = q · (L / 1000) · (B / 1000)

Column self-weight. For a rectangular section, the column mass is calculated from its height H, section dimensions b and h in mm, and material density ρ:

Mcolumn = (H / 1000) · (b / 1000) · (h / 1000) · ρ

For a standard steel profile, its tabulated mass per metre is multiplied by the column height. The permanent component also includes the self-weight of the main beam and, where applicable, secondary beams; all these components are multiplied by 1.35.

Total column load. The total design load on the column is obtained by summing the self-weight of the column and beams, permanent loads from the tributary area, partition loads, and the governing combination of variable loads. The result is displayed in kg and kN.

Assumptions used

Uniform load distribution. Loads from layers, partitions, snow, and imposed load are assumed to be uniformly distributed over the corresponding area. For beam calculations, the area load is converted into a uniformly distributed line load using the tributary width.

Fixed design factors. Permanent loads use γ_G = 1.35, and the leading variable action uses γ_Q = 1.50. For an accompanying imposed load, ψ_0,Q = 0.70 is used, while ψ_0,S for snow is entered by the user and defaults to 0.50.

National values. Snow loads, imposed-load categories, and combination factors may differ between National Annexes to the Eurocodes. Characteristic input loads and, where necessary, ψ_0,S should therefore be selected for the country and conditions of the specific project.

FAQs

Why is the factor for snow or imposed load sometimes lower than 1.50?

When two variable loads act simultaneously, only one is treated as the leading action and receives the full factor 1.50. The accompanying action is additionally reduced by ψ₀: for imposed load, ψ₀ = 0.70 gives an effective factor of 1.05, while snow uses the specified ψ_0,S value.

How does the calculator decide whether snow load or imposed load is leading?

Both combinations are calculated automatically: first with the imposed load as leading, then with the snow load as leading. The calculator compares the resulting total design loads and uses the larger value, so the choice does not depend simply on which characteristic load is numerically greater.

What snow and imposed load values should be entered?

Enter characteristic values before applying the factors 1.35 or 1.50. Snow load should be determined according to EN 1991-1-3 and the applicable National Annex, while imposed load should be selected by occupancy category according to EN 1991-1-1; the load calculation calculator applies the design factors automatically.

How is an area load converted into a beam load?

The load in kg/m² is multiplied by the beam spacing in metres, which represents the width of the tributary strip carried by the beam. This produces a line load in kg/m; multiplying it by the beam length gives the total load in kg.

How are partition loads included?

Their total mass is first calculated from the total length, thickness, height, and material density. This mass is then uniformly distributed over the considered area, and the resulting area load is treated as a permanent load with a factor of 1.35.