📐 Structural Engineering

Beam Load Calculator

Q: What is UDL (Uniformly Distributed Load)?

A Uniformly Distributed Load (UDL) is a load 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 plus 1–2 kN/m² dead load, typically 15–25 kN/m total beam load.

Calculate reactions, maximum bending moment, shear force, and deflection for simply supported, cantilever, and fixed beams — with point and UDL loads.

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Beam Load Calculator

Simply Supported · Cantilever · Fixed Both Ends

Simply Supported Beam with Uniformly Distributed Load (UDL)

Beam Span L (m) Clear span between supports

Beam Width b (mm) Width of beam cross-section

Beam Depth D (mm) Overall depth of beam

Load Type

UDL Intensity w (kN/m) Total load per meter of beam

Point Load P (kN) Concentrated load at mid-span

Concrete Grade

Self Weight Include?

📊 Calculation Results

✅ Calculated

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Reaction RA

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Reaction RB

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kN·m

Max Moment M

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Max Shear V

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Max Deflection

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kN/m

Self Weight

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📖 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)

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

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.