Engineering
Beam Bending Capacity Calculator
Calculate nominal and safety-factor-adjusted bending moment, total uniform-load capacity, dead- and live-load allowance, tributary area load, support reaction, comparison utilization, and margin.
Nominal yield moment capacity-
Capacity after entered safety factor-
Total uniform load at allowable moment-
Entered beam and other dead load-
Uniform live-load capacity after dead load-
Entered live load plus dead load as capacity share-
Remaining live load divided by tributary width-
End reaction at total allowable uniform load-
Remaining live-load capacity minus comparison-
Decision view
Beam load, moment, and capacity diagram
Beam load, moment, and capacity diagramUniform load, idealized support reactions, the midspan moment curve, and comparison utilization update together.
Exact scenario comparisonMaterial yield strength (MPa) changes while all other entered assumptions remain constant.
| Material yield strength (MPa) | Nominal yield moment capacity | Capacity after entered safety factor | Total uniform load at allowable moment | Entered beam and other dead load | Uniform live-load capacity after dead load | Entered live load plus dead load as capacity share | Remaining live load divided by tributary width | End reaction at total allowable uniform load | Remaining live-load capacity minus comparison |
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How to use Beam Bending Capacity Calculator
- Enter section modulus, yield strength, and the intended preliminary safety factor.
- Enter span plus beam and other dead line loads.
- Enter a live-load comparison and tributary width.
- Read the force diagram, capacity line, utilization, and support reactions together.
Calculator guide
Understanding Beam Bending Capacity Calculator
A beam's elastic section modulus and yield strength define a nominal yield moment. This preliminary model applies an entered safety factor, back-solves the uniform load for a simply supported span, and then separates dead load from remaining live-load allowance.
Calculation method
How the calculation works
Convert section modulus and yield strength into nominal moment, divide by an explicit safety factor, and back-solve a simply supported uniform-load capacity before dead-load deduction. Multiply elastic section modulus by yield strength, convert N·mm to kN·m, divide by the entered safety factor, use M=wL²/8, and deduct the entered dead loads.
Detailed calculation process
Back-solve a uniform load from elastic bending capacity
The default uses Z=650,000 mm³, yield strength 250 MPa, safety factor 1.5, span 6 m, 1.85 kN/m total dead load, and a 6 kN/m comparison live load.
General formula: M_n = Zf_y/10⁶M_a = M_n/γw_a = 8M_a/L²w_D = w_b+w_ow_L = max(w_a-w_D,0)U = 100(w_D+w_c)/w_aq_L = w_L/b_tR = w_aL/2 MPa equals N/mm², so section modulus times yield strength gives N·mm and is divided by one million for kN·m. The simply supported uniform-load moment equation is inverted, after which dead load is reserved before live-load capacity is reported.
What each symbol means
Worked substitution with the default inputs
The defaults produce 162.5 kN·m nominal moment, 108.333 kN·m after the entered factor, 24.074 kN/m total uniform-load capacity, and 22.224 kN/m remaining live-load allowance.
Bending mechanics
Connect the load diagram to the moment-capacity check
The engineering view shows uniform load, equal support reactions, the parabolic moment diagram, and the comparison point against the entered-factor capacity.
Worked situations
Practical examples
- The section properties produce 162.5 kN·m nominal yield moment.
- A 1.5 safety factor reduces the entered-factor capacity to 108.333 kN·m.
- After 1.85 kN/m dead load, 22.224 kN/m remains for live load in this simplified model.
Better inputs
Useful tips
- Use section modulus about the actual bending axis.
- Keep characteristic, allowable, and factored load conventions from being mixed.
- Check shear, deflection, vibration, stability, and connections separately.
Before relying on the result
Limitations and common mistakes
- This is not a code-compliant strength or serviceability design.
- Lateral-torsional buckling, plasticity, holes, composite action, shear, deflection, vibration, fire, fatigue, and connections are excluded.
- Loads, combinations, resistance factors, safety factors, and material properties require qualified selection.
Reference
Key terms
- Section modulus
- Elastic geometric property relating bending moment to extreme-fibre stress.
- Uniform line load
- Load distributed along beam length in kN/m.
- Tributary width
- Width used to convert beam line load to an area-load reference.
- Support reaction
- Vertical force carried by a support under the modeled load.
Important note
Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.
Frequently asked questions
Is this a structural design approval?
No. It is a transparent preliminary bending calculation only.
Why is dead load deducted before live load?
Dead load already uses part of the total uniform-load capacity.
Why divide by tributary width?
It converts the remaining beam line load into an equivalent area-load reference.
Does 32.6% utilization mean the beam is safe?
No. Other limit states, load combinations, code factors, and actual details still require review.