Prestressed Concrete Beam Calculator: Fibre Stresses and Prestress Force

Fibre stresses in a simply supported rectangular prestressed beam, or the prestress force and eccentricity that give wanted stresses.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the section, the span, the total load and the prestress force and its eccentricity below the centroid. The calculator works out the midspan moment from the load, then the stress at the top and bottom fibres from the load and from the prestress, and adds them. Compression is negative and tension is positive.

The other mode works backwards. Enter the stresses you want at the top and bottom fibres. The average of the two gives the prestress force and half the difference gives the moment, so it also gives the eccentricity e = M/P.

Check the result against the allowable stresses for the concrete. Losses of prestress, the stresses at transfer, shear and ultimate strength are separate checks.

Formulas used

  • f = -\frac{P}{A} \pm \frac{Pec}{I} \mp \frac{Mc}{I}
  • M = \frac{wL^2}{8}
  • e = \frac{M}{P}

Worked example

With the default numbers in the calculator above:

  1. Area and second moment of area: 120000.00 mm²
  2. Bending moment from the load at midspan: 180.00 kN·m
  3. Stress at the top fibre from the load: -15.00 MPa
  4. Stress at the bottom fibre from the load: 15.00 MPa
  5. Moment from the prestress force: 240.00 kN·m
  6. Stress at the top fibre from the prestress: 10.00 MPa
  7. Stress at the bottom fibre from the prestress: -30.00 MPa
  8. Total stress at the top fibre: -5.00 MPa
  9. Total stress at the bottom fibre: -15.00 MPa

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? The prestress force and eccentricity from the fibre stresses; Width of the beam 300 mm.

  1. Area and second moment of area: 180000.00 mm²
  2. Average stress gives the prestress force (the same at every fibre from the force alone): 900.00 kN
  3. Difference gives the bending moment about the centroid (Pe plus any load moment): 126.00 kN·m
  4. Eccentricity of the force: 140.00 mm

Common questions

Why put the tendon below the centroid?

The prestress then bends the beam upward, which opposes the sag from the load, and puts compression where the load puts tension.

Is this the stress at the ends too?

No. It is at midspan. At the ends the load moment is zero, so check them separately.

What signs does it use?

Compression negative, tension positive.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS 3600 (concrete structures, prestressed members); Nilson, Design of Prestressed Concrete.

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