Skip to main content

ASTM strand

The ASTM A 416 defines a stress-strain curve doe seven-wire strands. This has an initial linear relationship up to a strain of 0.008 with progressive yield till failure.

ASTM strand diagram of stress-strain curve defined.

The stress strain curves are defined for specific strengths.

For Grade 250 1^1 (1725 MPa) the stress-strain curve is defined as

σ=197000ε                      ε ≤ 0.008\sigma= 197000\varepsilon \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \varepsilon \space \leq \space 0.008
σ=1710−0.4ε−0.006      ε>0.008\sigma= 1710-\frac{0.4}{\varepsilon-0.006} \space \space \space \space \space \space \varepsilon > 0.008

For Grade 270 (1860 MPa) the stress-strain curve is defined as

σ=197000ε                      ε ≤ 0.008\sigma= 197000\varepsilon \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \varepsilon\space \leq\space0.008
σ=1848−0.517ε−0.003      ε>0.008\sigma= 1848-\frac{0.517}{\varepsilon-0.003} \space \space \space \space \space \space \varepsilon>0.008

In the Commentary to the Canadian Bridge 2^2 code a similar stress-strain relationship is defined.

For Grade 1749 strand

σ=Epε                              ε ≤ 0.008\sigma= E_p\varepsilon \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \varepsilon\space \leq\space0.008
σ=1749−0.433ε−0.00614      ε>0.008\sigma=1749-\frac{0.433}{\varepsilon-0.00614} \space \space \space \space \space \space\varepsilon>0.008

For Grade 1860 strand

σ=Epε                              ε ≤ 0.008\sigma=E_p\varepsilon \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \varepsilon \space \leq \space 0.008
σ=1848−0.517ε−0.0065      ε>0.008\sigma=1848-\frac{0.517}{\varepsilon-0.0065}\space \space \space \space \space \space\varepsilon>0.008

A more detailed discussion of modelling strands can be found in the paper by Devalapura and Tadros 3^3.

Endnotes​

  1. Bridge Engineering Handbook, Ed. Wah-Fah Chen, Lian Duan, CRC Press 1999.

  2. Commentary on CSA S6-14, Canadian Highway Bridge Design Code, CSA Group, 2014.

  3. Stress-Strain Modelling of 270 ksi Low-Relaxation Prestressing Strands, Devalapura R K & Tadros M K, PCI Journal, March April 1992.