# What does cross section area mean when dealing with stress/strain?

1. Apr 4, 2014

### Jay520

What does "cross section area" mean when dealing with stress/strain?

1. The problem statement, all variables and given/known data

For clarification, here is an example problem:

A circular steel wire 2 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?

Relevant equations

FL = YA(ΔL)

Apparently, the cross section area for this object is simply pi*r^2 (as for any circle). Can someone tell me exactly what the cross section area is supposed to refer to? I thought it was the area of the plane of the object perpendicular to the applied force, but apparently I'm wrong or not understanding something properly.

Last edited: Apr 4, 2014
2. Apr 4, 2014

### Staff: Mentor

Why do you feel that you are wrong or not understanding something properly?

Chet

3. Apr 4, 2014

### Jay520

I don't know what the definition of "cross section area" is. At least not well enough to apply it to the context of elasticity physics problems.

4. Apr 4, 2014

### SteamKing

Staff Emeritus
When you put the wire in tension, the tensile stress is calculated using the circular cross-section of the wire.
The tensile stress σ = F/A, where F is the tensile load (Newtons) and A is the cross section area (m^2), and the stress σ has units of pascals (N/m^2)

For a circular wire, A = πR$^{2}$ or πD$^{2}$/4, where R (radius) or D (diameter) of the wire are measured in meters.

The elongation of an object undergoing a tensile load is

δ = FL/AE

where

L = unloaded length of the object (meters)
A = cross sectional area of the object (m^2)
E = modulus of elasticity of the material (Pa)

The cross section just refers to the shape of the loaded object which results from its intersection with a plane oriented normal to the applied load.

5. Apr 4, 2014

### Staff: Mentor

For a long cylindrical body (not necessary a circular cylinder), the cross sectional area is obtained by cutting the cylinder with a knife perpendicular to its axis and looking in at the exposed area. The area that is exposed is the cross sectional area of the cylinder.

Chet