Equation Pad

Equation Pad › Library › Eurocode 2 › Serviceability

Stresses in a cracked rectangular section

Neutral axis depth, second moment of area of the cracked section and the stresses in concrete and steel. Reference: EN 1992-1-1 7.1, 7.2.

Open this sheet in Equation Pad Browse the Library

Stresses in a cracked rectangular section: worked example sheet in Equation Pad with typeset equations and results.

Example only. This sheet shows one way to set out the check. It is not endorsed by the bodies that publish the design codes and does not reproduce them. Check every clause, value and assumption against your own copy of the current edition of Eurocode 2 and its national annex before you use it, and have the result checked by a competent person. See the disclaimer.

The calculation, line by line

Every line below is typed into Equation Pad exactly as shown; the app typesets it, works out the value with its units and shows checks as TRUE or FALSE. Change any input and everything below it updates.

# Inputs
b := 1000 mm
d := 200 mm
A_s := 1131 mm^2
M := 45 kN*m
E_s := 200 GPa
E_cm := 33 GPa
phi_cr := 2.0

# Section
alpha_e := E_s/(E_cm/(1 + phi_cr)) =
x := (-alpha_e*A_s + sqrt((alpha_e*A_s)^2 + 2*b*alpha_e*A_s*d))/b = mm
I_cr := b*x^3/3 + alpha_e*A_s*(d - x)^2 = mm^4

# Stresses
sigma_c := M*x/I_cr = MPa
sigma_s := alpha_e*M*(d - x)/I_cr = MPa

How to use this example

  1. Click Open this sheet in Equation Pad. It opens as a new worksheet in your browser; nothing is installed.
  2. Change the inputs at the top to those of your project.
  3. Check the clauses and coefficients against the code, add your own checks, and save the sheet or export a PDF with your title block.

More Eurocode 2 sheets on serviceability

The same topic in IS 456