Structural Engineering
Beam Load Calculator
Calculate reactions, maximum bending moment, shear force, and deflection for simply supported, cantilever, and fixed beams — with point and UDL loads.
Beam Load Calculator
Simply Supported · Cantilever · Fixed Both Ends
Simply Supported Beam with Uniformly Distributed Load (UDL)
Clear span between supports
Width of beam cross-section
Overall depth of beam
Total load per meter of beam
Calculation Results
Calculated—
kN
Reaction RA
—
kN
Reaction RB
—
kN·m
Max Moment M
—
kN
Max Shear V
—
mm
Max Deflection
—
kN/m
Self Weight
—
How the Beam Load Calculator Works
This calculator computes the structural responses of beams under various loading conditions using standard structural engineering formulas from ACI 318, BS 8110, and IS 456.
Simply Supported Beam — UDL
RA = RB = w × L / 2
Maximum Moment (at mid-span): M = w × L² / 8
Maximum Shear (at supports): V = w × L / 2
Maximum Deflection (at centre): δ = 5wL⁴ / 384EI
Self Weight: sw = b × D × 25 kN/m³ (unit weight of RCC)
Maximum Moment (at mid-span): M = w × L² / 8
Maximum Shear (at supports): V = w × L / 2
Maximum Deflection (at centre): δ = 5wL⁴ / 384EI
Self Weight: sw = b × D × 25 kN/m³ (unit weight of RCC)
Cantilever Beam — UDL
Reaction at fixed end: R = w × L
Maximum Moment (at fixed end): M = w × L² / 2
Maximum Shear (at fixed end): V = w × L
Maximum Deflection (at free end): δ = wL⁴ / 8EI
Maximum Moment (at fixed end): M = w × L² / 2
Maximum Shear (at fixed end): V = w × L
Maximum Deflection (at free end): δ = wL⁴ / 8EI
E (Modulus of Elasticity) = 5000 × √fck MPa (as per IS 456) · I = bD³/12 (Moment of Inertia)
These results are for preliminary estimation only. All structural beams must be verified and designed by a licensed Structural Engineer before construction.
Standard Beam Span-to-Depth Ratios
Recommended L/D ratios for initial beam depth selection (before detailed design):
| Beam Type | Loading | Span/Depth Ratio | Example: 5m Span |
|---|---|---|---|
| Simply Supported Slab | Light | 20 – 26 | D = 192–250 mm |
| Simply Supported Beam | Moderate | 12 – 15 | D = 333–417 mm |
| Continuous Beam | Moderate | 15 – 20 | D = 250–333 mm |
| Cantilever Beam | Light | 7 – 10 | D = 500–714 mm |
| Fixed Both Ends | Heavy | 10 – 12 | D = 417–500 mm |
Frequently Asked Questions
A bending moment is the internal moment that causes a beam to bend. It is measured in kN·m or kip·ft. At any cross-section, the bending moment equals the sum of moments of all forces acting on one side of that section. The maximum bending moment determines the required steel reinforcement and concrete dimensions.
A Uniformly Distributed Load (UDL) is a load that is spread evenly along the entire length of a beam — like the weight of a floor slab, wall, or roof. It is measured in kN/m. Common UDL values for residential slabs in Pakistan: 3–5 kN/m² live load + 1–2 kN/m² dead load = typically 15–25 kN/m total beam load.
For a typical 5-meter residential beam in Pakistan with moderate loading (20 kN/m), a standard size is 230mm × 450mm (width × depth) using M20 concrete. The exact size must be confirmed by structural design considering actual loads, steel reinforcement, and site conditions.
Self weight (sw) = b × D × unit weight of RCC = b(m) × D(m) × 25 kN/m³. For a 230mm × 450mm beam: 0.23 × 0.45 × 25 = 2.59 kN/m. This must be added to the imposed loads before calculating reactions and moments.
