Beam Calculator: Bending Moment, Shear Force and Deflection
Calculate bending moments, shear forces, and deflections for structural beams. Supports simply supported, cantilever, and fixed-end conditions with visual moment and shear diagrams.
Last updated: January 2026
Steel: 200,000 MPa, Concrete: ~25,000 MPa
Required for deflection calculation
Max Moment
90kN·m
Max Shear
60kN
Deflection
16.88mm
Moment in kN·m, position in m. Positive moment = tension at bottom (sagging)
Shear in kN, position in m. Positive shear = upward force on left of section
Left Reaction (R₁)
60 kN
Right Reaction (R₂)
60 kN
Notes:
- Moments, shears and reactions only - this tool does not size or check a member. Section selection needs bending, shear, lateral-torsional buckling and deflection checks by a qualified engineer.
- Cantilever and fixed-pinned: fixed support at the left end; point-load position measured from the left support
- Verify with detailed structural calculations
- Consider load combinations per applicable code
- The deflection limit is set by the governing code and the project specification
- Deflection is calculated only for simply supported (uniform or central point load), cantilever (uniform) and fixed-both-ends (uniform or central point load) cases; other cases show N/A
IMPORTANT DISCLAIMER
This calculator provides PRELIMINARY ESTIMATES ONLY and is intended for planning and budgeting purposes. Results should NOT be used for final structural design or construction without verification by a licensed Professional Engineer (PE) or Chartered Engineer (CEng).
By using this tool, you acknowledge that:
1. All calculations are indicative and may not account for site-specific conditions, load combinations, or local code requirements.
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About This Calculator
The Beam Load Calculator helps structural engineers analyze and design beams for buildings and infrastructure across the UAE and Gulf. Calculate bending moments, shear forces, and deflections for various support conditions and load types. Essential for preliminary beam sizing, checking existing designs, and understanding load distribution in concrete and steel structures.
Formula
Simply supported, UDL w: R = wL/2; M(x) = w x (L - x) / 2; Mmax = wL^2/8; Vmax = wL/2
Simply supported, point load P at a (b = L - a): R1 = P b / L; R2 = P a / L; Mmax = P a b / L
Cantilever (fixed at left), UDL: R = wL; Mmax = wL^2/2; Vmax = wL
Cantilever, point load P at a: R = P; Mmax = P a
Fixed both ends, UDL: end moments wL^2/12; midspan wL^2/24
Fixed-pinned (fixed left), UDL: fixed-end moment wL^2/8; reactions 5wL/8 and 3wL/8; maximum span moment 9wL^2/128 at x = 5L/8
Fixed ends with a point load use the standard fixed-end moment expressions, for example P a b^2 / L^2 at the left end
Maximum moment and shear are the largest absolute values found at 21 evenly spaced stations plus the load position
Deflection (needs I): simply supported UDL 5wL^4 / (384 E I); simply supported central point load P L^3 / (48 E I); cantilever UDL wL^4 / (8 E I); fixed-both-ends UDL wL^4 / (384 E I); fixed-both-ends central point load P L^3 / (192 E I)
Worked example
Inputs
- Span 6 m, simply supported
- Uniformly distributed load 20 kN/m
- E = 200,000 MPa (steel)
- I = 10,000 cm4
Steps
- Total load W = 20 x 6 = 120 kN, so each reaction = 120 / 2 = 60 kN
- Maximum moment = wL^2/8 = 20 x 6^2 / 8 = 90 kN·m at midspan
- Maximum shear = wL/2 = 60 kN at the supports
- Deflection = 5 x 20 x 6^4 / (384 x 200,000,000 kPa x 0.0001 m4) = 0.01688 m = 16.88 mm
Result: Reactions 60 kN each, maximum moment 90 kN·m, maximum shear 60 kN and 16.88 mm elastic deflection (about span/355). This is the load effect only; the member still has to be checked.
Assumptions and limits
- Linear-elastic, prismatic beam with one constant E and I; self-weight is not added automatically, so include it in the load you enter.
- Loads are used as entered: no load factors or combinations are applied.
- For the cantilever and fixed-pinned options the fixed support is at the left end.
- The tool gives moments, shears, reactions and, for the cases listed above, an elastic deflection. It does not size or check a member; bending, shear, lateral-torsional buckling, bearing and deflection-limit checks are still needed.
- Deflection is shown as N/A for combinations without a formula (for example a point load at an arbitrary position, or a fixed-pinned beam).
- Shear and moment diagrams are sampled at 21 points plus the load position, so peaks between stations are only exact for the load cases above.
- Check the governing code and project specification for load combinations and serviceability limits. This is a preliminary check, not a substitute for a qualified engineer's design.
When to Use This Calculator
- Getting moments, shears and reactions as inputs for beam design
- Analyzing load effects for steel beam selection
- Checking deflection limits against serviceability requirements
- Understanding moment and shear distribution for complex loads
- Verifying hand calculations before detailed analysis
How to Use This Calculator
Select Support Conditions
Choose beam type: simply supported, cantilever, fixed both ends, or fixed-pinned (propped cantilever).
Enter Beam Geometry
Input the span length and, optionally, the section's second moment of area (I) for deflection.
Define Loads
Enter a uniformly distributed load (UDL) or a single point load at mid-span or at any position.
Specify Material
Select material properties (E modulus) for deflection calculations.
View Results
Get maximum moment, shear, deflection, and visual diagrams for the beam.
Typical Scenarios in UAE & Gulf Projects
A 6m span floor beam carries 45 kN/m UDL from slabs and partitions. The calculator shows maximum moment 202.5 kNm at mid-span and maximum shear 135 kN at the supports. Deflection also needs E and I for the chosen section. These are load effects only: the engineer then designs and checks the member.
A 12m simply supported steel beam carries a 15 kN/m UDL. The calculator gives a 270 kNm maximum moment at mid-span and 90 kN reactions. The structural engineer then selects and checks the steel section (bending, shear, lateral-torsional buckling and deflection); the tool does not size the member.
Frequently Asked Questions
What are the deflection limits for beams?
Deflection limits are set by the governing code, the project specification and what the beam supports (brittle finishes and sensitive equipment need tighter limits). They are usually written as a fraction of the span, such as L/250 or L/360, and differ between codes and between floor beams and cantilevers. This tool gives the elastic deflection of the cases it supports; long-term effects such as creep must be added by the engineer.
How do I calculate simply supported beam moment?
For simply supported beams: Point load at center: M = PL/4. UDL: M = wL²/8. Point load at distance 'a' from support: M = Pa(L-a)/L at load point. Multiple loads: superimpose individual moments. Maximum shear typically at supports = R (reaction).
What beam depth ratio should I use for preliminary sizing?
Rule-of-thumb span-to-depth ratios for preliminary design: Simply supported RC beam L/12 to L/15, Continuous RC beam L/15 to L/20, Steel beam L/20 to L/24, Cantilever L/6 to L/8. Deeper beams reduce deflection; shallower beams need more reinforcement. These are rules of thumb only; the engineer sizes the member.
Last Updated: January 2026
Standards Reference: Elastic beam formulas (moments, shears, reactions); member design per ACI 318-19 or BS EN 1992 by a qualified engineer
