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Prestressed Concrete Camber & Deflection Calculator

Prestressed and precast concrete bridge girders experience initial upward camber when pretensioned tendons release eccentric prestressing forces into the beam.

Center-to-center span length between bearing supports (typically 10 to 45 m).

Net effective prestressing force after release relaxation losses.

Vertical distance between the concrete cross-section centroid and strand centroid.

Modulus of elasticity at release (typically 28 to 38 GPa for high-performance concrete).

Gross second moment of area of the concrete beam section.

Dead weight uniform load per unit span length of the girder.

Calculated Result
2.3 mm

Net Initial Release Camber

Net Initial Release Camber

2.3 mm (Upward Camber)

Long-Term Creep Camber (PCI)

3.8 mm

Prestress Upward Thrust (Δ_p)

+8.4 mm

Self-Weight Dead Load Sag (Δ_sw)

-6.2 mm

Beam Span

18 m (59.1 ft)

Calculation Breakdown

  1. Prestress Internal Upward Bending CamberΔ_p = (P × e × L²) / (8 × E_c × I) = (1200 kN × 0.25m × 18²) / [8 × 32 GPa × 0.045] = +8.4 mm
  2. Beam Self-Weight Downward Elastic DeflectionΔ_sw = (5 × w × L⁴) / (384 × E_c × I) = (5 × 6.5 kN/m × 18⁴) / [384 × 32 GPa × 0.045] = -6.2 mm
  3. Net Erection Camber & Martin PCI Creep MultiplierNet Camber = 8.4 - 6.2 = 2.3 mm → Long-Term = 1.8(Δ_p) - 1.85(Δ_sw) = 3.8 mm

Beam Vertical Displacement Profile (mm)

Interactive visualization based on your current inputs

Displacement
-6.1-2.51.24.88.4Upward PrestressDownward Self-WeightNet InitialLong-Term Est.ComponentDisplacement (mm)

What Is the Prestressed Concrete Camber & Deflection Calculator?

The Prestressed Concrete Camber & Deflection Calculator evaluates instantaneous and long-term vertical deflections of pretensioned structural girders.

How Does the Prestressed Concrete Camber & Deflection Calculator Work?

It combines internal prestress moments with gravity self-weight deflections using elastic beam mechanics, applying PCI multipliers for creep progression.

Prestressed Concrete Camber & Deflection Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\Delta_p = \frac{P \cdot e \cdot L^2}{8 E_c I}, \quad \Delta_{sw} = \frac{5 w_{sw} L^4}{384 E_c I}, \quad \Delta_{net} = \Delta_p - \Delta_{sw}

Superposition of eccentric axial tendon internal bending moment against gravity dead load deflection.

How to Use the Prestressed Concrete Camber & Deflection Calculator

  1. Enter girder span length and effective prestress force.
  2. Input strand eccentricity from cross-section centroid.
  3. Specify concrete elastic modulus, section inertia, and self-weight.

Step-by-Step Example Calculation

18-Meter Precast I-Girder

Input Values:

beamSpanLengthM:18
prestressJackingForceKN:1200
tendonEccentricityMm:250
concreteElasticModulusGPa:32
beamMomentOfInertiaM4:0.045
beamSelfWeightKNPerM:6.5
Worked Steps: Generates 8.44 mm upward prestress camber minus 6.13 mm self-weight deflection, leaving +2.31 mm net initial camber.

Understanding Your Result

Upward Camber: Upward displacement driven by tendon eccentricity.

Self-Weight Deflection: Downward sag due to beam gravity dead load.

Net Initial Camber: As-erected elevation crown at transfer.

Long-Term Camber: Anticipated crest elevation after creep and shrinkage maturation.

Factors That Affect the Result

  • Higher tendon eccentricity significantly magnifies upward camber.
  • Lower release concrete strength (lower Ec) increases initial camber and subsequent creep growth.

When Should You Use This Calculator?

  • Bridge girder design, precast parking structure double-tees, architectural haunching, and deck slab screed profiling.

Assumptions & Limitations

  • Assumes straight constant-eccentricity tendon layout across a prismatic uncracked section.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Adheres to PCI Design Handbook (8th Edition) and AASHTO LRFD specifications.

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