Bending analysis
of beams using BendIT©
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To enable quick and easy calculation of various load cases, BendIT is now available directly as an online calculator. Select the profile, dimensions and load case; the calculation is carried out directly in the browser.
The calculated values are provided for guidance only during preliminary design and do not replace a project-specific structural analysis. Despite careful implementation, the calculator may produce incorrect results; inputs, load assumptions and results must be checked by a qualified professional before use.
Enter the profile type and dimensions, select the load case and calculate the key parameters directly.
Section and dimensions
<select id="bendit-profile" data-bendit-input="profile">
<option value="solid-round">Solid bar</option>
<option value="tube-round">Tube</option>
<option value="flat">Flat profile</option>
<option value="rect-tube">Rectangular tube</option>
<option value="i-profile">I-section</option>
<option value="h-profile">H-section</option>
<option value="u-profile">U-section</option>
<option value="u-profile-head">U-section end</option>
<option value="u-profile-side">U-section, side view</option>
<option value="angle">Angle</option>
<option value="t-profile">T-profile</option>
<option value="t-profile-head">T-profile top</option>
<option value="manual">Manual profile parameters</option>
</select>
<input id="bendit-width" data-bendit-input="width" type="number" min="1" step="1" value="60">
<input id="bendit-height" data-bendit-input="height" type="number" min="1" step="1" value="100">
<input id="bendit-inner-width" data-bendit-input="innerWidth" type="number" min="0" step="1" value="60">
<input id="bendit-inner-height" data-bendit-input="innerHeight" type="number" min="0" step="1" value="25">
<input id="bendit-wall" data-bendit-input="wall" type="number" min="0" step="0.5" value="5">
<input id="bendit-flange" data-bendit-input="flange" type="number" min="0" step="0.5" value="8">
<input id="bendit-diameter" data-bendit-input="diameter" type="number" min="1" step="1" value="80">
<input id="bendit-inner-diameter" data-bendit-input="innerDiameter" type="number" min="0" step="1" value="50">
Load case and load
<select id="bendit-case" data-bendit-input="case">
<option value="bending-point">Bending: Single load centred</option>
<option value="bending-line">Bending: Uniformly distributed load</option>
<option value="compression">Compression / Buckling</option>
<option value="tension">Tension</option>
<option value="torsion">Torsion</option>
<option value="wind">Wind load</option>
</select>
<input id="bendit-force" data-bendit-input="force" type="number" min="0" step="10" value="1000">
<input id="bendit-line-load" data-bendit-input="lineLoad" type="number" min="0" step="0.1" value="2">
<input id="bendit-length" data-bendit-input="length" type="number" min="1" step="10" value="1000">
<input id="bendit-e" data-bendit-input="eModulus" type="number" min="1" step="100" value="23000">
<input id="bendit-g" data-bendit-input="gModulus" type="number" min="1" step="100" value="3500">
<input id="bendit-area" data-bendit-input="area" type="number" min="1" step="10" value="1000">
<input id="bendit-inertia" data-bendit-input="inertia" type="number" min="1" step="1000" value="1200000">
<input id="bendit-section" data-bendit-input="section" type="number" min="1" step="100" value="24000">
<input id="bendit-torsion-section" data-bendit-input="torsionSection" type="number" min="1" step="100" value="18000">
<input id="bendit-polar" data-bendit-input="polar" type="number" min="1" step="1000" value="850000">
<input id="bendit-torque" data-bendit-input="torque" type="number" min="0" step="100" value="50000">
<input id="bendit-wind-speed" data-bendit-input="windSpeed" type="number" min="0" step="1" value="25">
<input id="bendit-wind-area" data-bendit-input="windArea" type="number" min="0" step="0.01" value="1">
For standard profiles, the cross-sectional area A, the area moment of inertia I and the section modulus W are calculated from the dimensions. To obtain exact catalogue values, you can switch to manual profile characteristics.
<button type="button" data-bendit-reset>Standard values</button>
Result
Bending stress-
Deflection-
Bending moment-
Calculation is loading.
The calculated values are provided for guidance only for preliminary dimensioning and do not replace a project-specific structural analysis. Despite careful implementation, the calculator may produce incorrect results; inputs, load assumptions and results must be checked by a qualified professional before use.
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Calculation of bending
In the bending analysis, the bending stress and deflection of a GRP section under transverse loading are estimated. The decisive factors are the load case, span, modulus of elasticity, and the section’s moment of inertia and section modulus.
Bending stress and deflection
σb =Mb /Wb
f = F ·L3 / (48 · E · I)
- σb = bending stress
- Mb = bending moment
- Wb = section modulus
- E = modulus of elasticity
- I = moment of inertia
Calculation of pressure
When subjected to compressive loading, the compressive stress and buckling resistance of the section are taken into account. The Euler buckling load serves as an idealised estimate for slender members and is not a substitute for a project-specific structural analysis.
Compressive stress and buckling load
σd = F / A
Fkrit =π² · E · I /lk²
- σd = compressive stress
- F = compressive force
- A = cross-sectional area
- Fkrit = critical buckling load according to Euler
- lk = buckling length
- E = modulus of elasticity
- I = moment of inertia
Torsion calculation
In the case of torsional loading, the torsional stress and angle of rotation of a section are estimated as a result of a torque. The decisive factors are the torsional moment, the shear modulus and the section properties relevant to torsion.
Torsional stress and angle of rotation
τ = T /Wt
φ = T · l / (G ·Jp)
- τ = torsional stress
- T = torsional moment
- Wt = moment of resistance to torsion
- φ = angle of rotation
- G = shear modulus
- Jp = polar moment of inertia
Wind load
FRP profiles subjected to wind loads are preliminarily dimensioned on the basis of the dynamic wind pressure and the exposed surface area. The wind speed determines the pressure, and this in turn determines the resulting wind force acting on the profile.
Wind pressure and wind force
q = 0.613 ·v²
Fw = q · A
- q = dynamic wind pressure [N/m²]
- v = wind speed [m/s]
- A = exposed area [m²]
- Fw = resulting wind force [N]
Calculation: Train
In the case of tensile loading, the tensile stress is calculated from the applied force and the effective cross-sectional area. This calculation is intended for rapid preliminary sizing and is not a substitute for a project-specific structural analysis.
Tensile stress
σz = F / A
- σz = tensile stress
- F = tensile force
- A = effective cross-sectional area