# Equations for Crack Width In Flexural Concrete Beams

There are many empirical equations have been developed for finding the maximum width of cracks. These equations were based on the statistical analysis of experimental result data. In ACI code, two expressions have been mentioned. The two expressions were developed by Gergely and Lutz and these expressions figured prominently the crack width at the tension face of a beam.

Expressions are;

$large w= 0.076beta f_{s}sqrt[3]{d_{c}A}$

$large w= 2000frac{f_{s}}{E_{s}}beta sqrt{d_{c}^{2} + (frac{s}{2})^{2}}$

Where;

W = maximum width of the crack

fs = stress in steel at which crack width is to be calculated (Ksi).

Es = elastic modulus of steel ( Ksi ).

The various geometric parameters are;

dc= thickness of concrete cover from tension side.

B(beta) = it is the ratio between h2/h1

A = concrete area surrounding by one bar of steel

S= maximum bar spacing, in.

These two equations are only for beams in which deformed bars are being used. The two expressions cover all the factors that have an important influence on the crack width. These factors are steel stress, concrete cover and steel distribution at tension side. B (beta) is the increment factor that is for increase in width of crack because of distance variation from the neutral axis.