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EurocodeCalculator

Calculator guide

Beam design calculator to Eurocode 2: rectangular, T and L beams

Design a reinforced concrete beam to EN 1992-1-1 with the free calculator: spans and sections, loads, bending, links, deflection and cracking.

Open the beam calculator

A reinforced concrete beam's steel cage with closed links on a building site
Reading time
4 minutes
Standard
EN 1992-1-1
Clauses
5.3.2, 6.1, 6.2, 7.3.3, 7.4.2, 9.2
Calculator
Beam
Updated
On this page 7 sections
  1. Beam type and spans
  2. The section
  3. Loads
  4. Bars and links
  5. What the calculator checks
  6. Reading the result
  7. Tips

The beam calculator designs a reinforced concrete beam to EN 1992-1-1: the bottom and top bars at every span and support, the links, and the checks for deflection and cracking. It takes characteristic loads per metre run, analyses the beam itself, and sets out the whole calculation with its clauses.

This guide explains each group of inputs and what the results mean. The beam design worked example follows the calculator's example beam through the bending design line by line.

Beam type and spans

  • Single span, pinned or fixed at each end.
  • Continuous, over two to six spans. The calculator analyses it by the stiffness method under every load arrangement the National Annex asks for, and designs for the envelope.
  • Cantilever, fixed at one end.

Enter the clear span of each span (between the faces of the supports) and the width of each support; the effective span adds half the support width, or half the depth if that is smaller, at each end (5.3.2.2).

The section

Three shapes are available:

ShapeInputsHow the flange is used
Rectangularweb width , depth
T-beamplus flange thickness and outstand each sidein compression at mid-span, with the effective width of 5.3.2.1
L-beamthe same, with the flange on one sideas for a T-beam

Over a support the flange is in tension, so the calculator designs the support section on the web alone. Beams deeper than a third of their span are deep beams, which need a different method; the calculator refuses them and says why.

The beam calculator's section and span inputs beside the long section of the example beam

The section and span inputs, with the drawing switched to the long section.

  1. Rectangular, T or L section; T and L take the flange too
  2. Web width and overall depth
  3. Clear span between the faces of the supports
  4. The long section: bars, links and where they stop

Loads

The loads are characteristic values per metre run of beam:

  • the superimposed dead load , to which the beam's own weight is added;
  • the use category and imposed load ;
  • an optional wind load, downward or uplift.

The calculator forms the ultimate combination by Expression 6.10 (or 6.10a and 6.10b), and the characteristic, frequent and quasi-permanent combinations for the serviceability checks. For the example beam (300 × 500 mm, 6000 mm clear span):

EN 1991-1-1 §5.2.1

Characteristic permanent load

gsup is the superimposed permanent load per metre run: the slab, finishes and walls carried by the beam.

= 18.750 kN/m
EN 1991-1-1 §6.3.1.2(1)P

Characteristic imposed load

= 12.00 kN/m
EN 1990 §6.4.3.2(3), Eq. (6.10)
EN 1990 §A1.3.1(4), Table A1.2(B)

6.10

= 43.313 kN/m
Design load on the beam (ULS)wd = 43.31 kN/mAleff,1 = 6.30 mBSelf-weight included. The analysis puts the patterned imposed load (load arrangements) on top of the permanent load.
Loading and supports. The largest ULS design load per metre run, on the supports the analysis uses.

With Choose bars for me, the calculator picks the lightest bars that pass bending, the minimum steel and the bar spacing rules, and the lightest links that pass shear. The deflection and cracking checks then run on those bars. With Enter my own bars you choose:

  • the number and diameter of the bottom bars, and of the top bars;
  • the link diameter, number of legs and spacing.

Bars are written as number, H and diameter, then B or T for the face: 1256.6 mm² of steel in the example comes from 4H20 B. Links are written as diameter, spacing and legs, such as H8 @ 325, 2 legs.

What the calculator checks

For each span and support, in this order:

What the beam calculator checks, section by section
  1. Loads, spans, and the envelope of every load arrangement
  2. Bending by the stress block (3.1.7), with a check that the tension steel yields
  3. Is x/d within the ductility limit of 5.5(4)?

    Yes

    1. Tension steel only

    No

    1. Compression steel as well
  4. Minimum and maximum steel (9.2.1.1), clear distance between bars (8.2)
  5. Shear: VRd,c, then links by the variable strut inclination method (6.2.3)
  6. Deflection by the span/effective depth ratio (7.4.2)
  7. Cracking under the quasi-permanent load (Tables 7.2N and 7.3N)
  8. Detailing: anchorage at the supports, laps, full-length top bars

The shear and links guide works through the shear step, with the minimum links and their spacing of 9.2.2.

Reading the result

The result header gives the bar schedule for every section, the links and the full-length top bars:

EN 1992-1-1 §6.1(2)P

Required tension reinforcement

= 1210.12 mm²
EN 1992-1-1 §9.2.1.1(1), Eq. (9.1N)
EN 1992-1-1 §8.2(2)

Bottom bars provided

4H20: one layer, 53 mm clear between bars. Fewest bars within 5 % of the lightest arrangement that fits. Considered: 4H20 (1257), 3H25 (1473), 2H32 (1608).

= 1256.6 mm² ✓ OK

The checks table lists every check with its utilisation; the highest is the one to watch. Beside it are the bending moment and shear force diagrams, with every load arrangement in grey and the envelopes on top.

Under the 3D model, the drawing shows the cross-section of each span, or, switched to Long section, the reinforcement along the beam: each bar and where it stops, the links and their spacing, and blue cuts marking where the cross-sections are taken.

Span 1Rectangular beam4H20 B2H12 T (hangers)H8 @ 325, 2 legsh = 500d = 460cnom = 22bw = 300Drawn to scale; dimensions in mm.
Cross-section: Span 1. Drawn to scale: links with cnom to their outer face, the main bars inside them; dimensions in mm.

Tips

  • A beam that fails deflection usually needs more depth, not more steel.
  • If the links come out very close, check against : a web that is too thin cannot be fixed with links.
  • For a continuous T-beam, look at the support sections: they are designed as rectangular, because the flange is in tension there.

Open the beam calculator and change any input to see every step worked out again.