Course · lesson 6 of 7

Crack width and deflection by calculation

How the STATIX crack width and deflection calculator works out cracking and deflection in service: when span/d is enough, cracked and uncracked sections, tension stiffening, creep and shrinkage, and crack width from the strain at the surface, on its SANS route (SANS 10100-1 Annex A, the BS 8110-2 method).

1. Learning outcomes

After this lesson you can:

say when span/d and bar spacing are enough and when to calculate;
find the cracking moment and the cracked section;
build the long-term deflection from creep, shrinkage and the loads;
work a crack width from the strain at the surface;
say which method the page used: Annex A / BS 8110-2 or EN 1992-1-1.

2. Before you start

RC Design 1, lesson 4 (span/d and bar spacing).
The crack width and deflection calculator.
A pocket calculator and about 60 minutes.

3. When and how

When span/d is enough. RC Design 1 checked deflection by span/d and cracking by bar spacing: quick, deemed-to-satisfy rules. They do not give a number for the deflection after the partitions are built or for a crack width, so calculate where finishes are brittle, members long or heavily loaded, the crack limit tight, or the member outside the rules.

The methods on the page. SANS 10100-1 sets its limits by span/d and bar spacing; its informative Annex A gives a calculation, which is the BS 8110-2 Part 2 method. The calculator’s SANS route, labelled “see note”, uses that Annex A method; the BS 8110-2 route is the same method; the EN 1992-1-1 route uses the Eurocode formulas. Say which you used.

4. Sections, stiffening and time

Cracked and uncracked sections. Below the cracking moment the whole section works; above it the concrete under the neutral axis cracks and the steel carries the tension. The calculator finds both transformed sections, with the steel converted to concrete by the modular ratio E_s/E_c.

Tension stiffening. Between cracks the concrete still carries some tension, so a cracked member is stiffer than the bare cracked section. Annex A and BS 8110-2 allow a triangle of concrete tension (1 MPa at the steel short-term, 0.55 MPa long-term) and take the larger curvature of the cracked and uncracked sets; EN 1992-1-1 interpolates between them with ζ.

Long-term effects. Under sustained load concrete creeps: its effective modulus falls to E_c/(1 + φ), so the curvature grows. Shrinkage adds a curvature of its own, ε_cs α_e S_s/I, because the steel restrains the shrinking concrete on one side. The calculator takes φ and ε_cs as inputs.

Deflection from curvature. The deflection is K l² times the curvature, K set by the supports and load shape. Annex A builds the long-term curvature from the permanent load long-term, plus the short-term part of the rest, plus shrinkage. The part that happens after the partitions is checked against a tighter limit; the page subtracts only the instant deflection before them, which is conservative.

5. Cracks and what helps

Where the crack is widest. A crack is narrow next to a bar and widens with distance from it; a_cr is the distance from the point considered to the surface of the nearest bar, usually at a bottom corner or midway between bars. Closer, smaller bars give narrower cracks.

Crack width. The strain at the surface ε₁ comes from the steel strain scaled to the tension face; the concrete between cracks reduces it to ε_m; the width then follows from a_cr. EN 1992-1-1 uses the crack spacing and the mean strain difference instead. The two give different numbers for the same beam.

Crack limits and the load. The limit depends on exposure and use; the page lets you choose it. On the SANS and BS routes the page takes the characteristic (total service) load G + Q, because SANS 10100-1 Annex A A.2.2.5 and BS 8110-2 3.6 build the short-term part from the total load; on the EN route it takes the quasi-permanent load G + ψ₂Q, as EN 1992-1-1 7.3 and 7.4 do. You can change the combination.

What helps. Extra tension steel lowers the steel stress, which narrows cracks and stiffens the cracked section; smaller bars at closer spacing narrow cracks further. Depth cuts deflection fastest. Building partitions later, or precambering, reduces the deflection that matters to them.

Uncertainty. A calculated deflection is only as good as its creep and shrinkage values and its E_c; vary them and see how much the answer moves. This lesson works the SANS route; the BS and EN routes are on the page too.