Material
Grade
Support type
Load
Height h, mm
Wall thickness t, mm
Flange width b, mm
Flange thickness h1, mm
Span L, mm
Calculation results:
Support type
Load
Height h, mm
Wall thickness s, mm
Flange thickness t, mm
Flange width b, mm
Span L, mm
Calculation results:
Support type
Load
Flange width a, mm
Flange width b, mm
Flange thickness t, mm
Span L, mm
Calculation results:
Support type
Load
Height h, mm
Width b, mm
Wall thickness t, mm
Span L, mm
Calculation results:
Useful calculators
About Beam Strength Calculation
The results are approximate. Before use, verify the calculations against the applicable standards and consult a specialist. The developer is not responsible for the consequences of use without project verification.
This calculator checks a beam for strength in bending and in shear. It determines the maximum internal forces for the selected structural scheme and load, then calculates stresses in the critical section and shows the safety margin for each criterion.
The calculation is available for steel and timber. Built-in numerical values for material resistance, density, and structural-scheme coefficients are used.
Guidelines and recommendations
Design approach. The calculation is based on the classical beam model and stress checks. Related Eurocode documents: EN 1990 (Basis of structural design), EN 1991-1-1 (Actions on structures), EN 1993-1-1 (Steel structures), EN 1995-1-1 (Timber structures).
Load unit conversion. When needed, the load is converted between kN and kg using a fixed factor:
1 kN = 101.971621 kg
This is used so that the applied load and the self-weight can be summed in consistent internal units.
Design resistance R. The checks use a value R in MPa. The calculator takes R from built-in values selected in the material list.
Steel. Built-in values (MPa): S235 = 197, S275 = 231, S355 = 298, S420 = 353.
Timber. Built-in base values (MPa): C16 = 8.62, C24 = 12.92, C30 = 16.15.
Factor 1.26. Only for a solid round timber section the calculator uses R = Rbase · 1.26. For other timber section types it uses R = Rbase.
Self-weight. Self-weight is added to the load as a uniformly distributed load along the beam length. The following densities are used:
- timber:
ρ = 700kg/m3 - steel:
ρ = 7850kg/m3
Section geometry. From the section dimensions the calculator determines area A (mm2), second moment of area I (mm4), and section modulus W (mm3). These values control the stresses for a given moment and shear force.
For a solid round section, standard formulas are used:
I = π·d4/64
W = π·d3/32
Maximum bending moment M. For a uniformly distributed load (including self-weight), the calculator applies a scheme coefficient m and calculates:
M = q · L2 · m
The coefficient m is selected from a built-in set: 0.08333333, 0.125, 0.125001, 0.5 (depending on the scheme).
For a point load, a scheme coefficient and a self-weight term are used:
M = P · L · k + Mg
Where k is selected from: 1/4, 5/32, 1/8, 1 (depending on the scheme), and Mg is the self-weight contribution.
Maximum shear force V. For a uniformly distributed load the calculator uses a relation of the form V = q · L · kV. In the calculation it applies kV = 1/2 or kV = 1 (depending on the scheme). For a point load, V is determined from scheme coefficients as a fraction of P.
Bending check. Normal bending stress is calculated as:
σ = M / W
The strength condition in bending is σ ≤ R. The bending safety margin is shown in percent relative to the limit R.
Shear check. Shear stress τ is calculated from the shear force V and the section geometry. The comparison uses a limit R · KRs, where the factor depends on the material:
- timber:
KRs = 0.10 - steel:
KRs = 0.58
The shear condition is τ ≤ R · KRs. The shear safety margin is shown in percent relative to the limit R · KRs.
Combined check (bending + shear). For some section types the calculator also computes an equivalent stress:
σeq = √(σ2 + 4·τ2)
And compares it to the limit:
σeq ≤ 0.87 · R
The purpose is to account for the influence of significant shear on the overall stress level. If, for the selected scheme, the calculator assumes that the maximum bending moment and the maximum shear do not occur at the same section, it may indicate that the combined check is not required.
Simplified slenderness check for profiles. For I-beams and channels the calculator evaluates slenderness using E = 206000 MPa. For the flange it uses the limit expression:
Yf,lim = 0.5 · √(206000 / R)
A threshold 2.5 is also used for the web. If the condition is not met, it is a practical indication that the profile is too slender for the selected material resistance.
FAQs
Which R values does the calculator use to compare stresses?
The calculator compares against R in MPa. For steel: 197, 231, 298, 353 (S235/S275/S355/S420). For timber: 8.62, 12.92, 16.15 (C16/C24/C30). For a solid round timber section it applies R = Rbase · 1.26.
Why are bending and shear checks shown separately?
Bending is governed by the moment M and produces stress σ. Shear is governed by the force V and produces stress τ. Depending on span, scheme, and load, either criterion can govern.
How is the beam self-weight included?
Self-weight is calculated from the section area, beam length, and density ρ. It is then converted into a uniformly distributed load and added to the applied load so that M and V are calculated including the beam weight.
What do the scheme coefficients 0.125, 0.08333333, 1/4 and others mean?
These are built-in coefficients for typical structural schemes. They define how the maximum bending moment and maximum shear are obtained from the load and the span. The calculator selects the coefficient for the chosen scheme and substitutes it into the formulas for M and V.
Why is the combined check σeq used, and what does 0.87 mean?
It accounts for the influence of shear on the overall stress level when bending and shear act together. The equivalent stress is calculated as σeq=√(σ²+4·τ²) and is compared to the limit 0.87·R, which is used in the calculator as an additional criterion.