# How Does Biaxial Force Affect Stress and Strain in a Rectangular Bar?

• Confusedbiomedeng
Also, the strain in the z direction is not necessary to solve for c', as there is no force applied in that direction. In summary, for a rectangular bar with dimensions a=b=2cm and c=20cm, subjected to biaxial forces Fx=Fy=0.4x106 N in the x and y directions, with an elastic modulus of E=100 GPa and a Poisson's ratio of u=0.3, the average normal stresses developed are σx=1x109 Pa and σy=-1x108 Pa. The average normal strains are ∈x=9.7 and ∈y=-2. To determine the new dimension c' in the x-direction after deformation, we can use
Confusedbiomedeng

## Homework Statement

consider the rectangular bar undeformed a=b=2cm and c=20cm . The elastic modulus of the bar material is E=100 Gpa and its poissons ratio is u=0.3. The bar is subjected to biaxial forces in the x and y directions such that Fx=Fy=0.4x106 N and that Fx is tensile while Fy is compressive . Assuming that the bar material is linear elastic
Determine:
i)the average normal stresses σx,σy and σz developed in the bar
ii)the average normal strains ∈x,∈y and ∈z
iii)dimension c' of the bar in the x-direction after deformation

## Homework Equations

σx=fx/(ab) σy=Fy/(cb) σz=no force no stress
∈x=1/E(σx-u(σy+oz))
∈y=1/E(σy-u(σx+σz))
∈z=1/E(σz-u(σx+σy))
∈=ΔL/L

## The Attempt at a Solution

σx=0.4x106/0.02x0.02=1x109
σy=0.4x106/0.2x0.02=1x108
σz=no force no stress

using above equation
∈x=9.7
∈y= -2
∈z= -3.3

new c dimension
.-3.3=ΔL/0.2
-0.66
0.2+-0.66= -0.46
however you can't have negative length??
can anyone show me where I am going wrong?

You forgot to divide by the Young's modulus, and the stress in the y direction is negative.

## 1. What are biaxial forces?

Biaxial forces are forces that act on an object in two different directions, known as the x-axis and y-axis. These forces can be either compressive or tensile, and their combined effect determines the overall stress on the object.

## 2. How do biaxial forces differ from uniaxial forces?

Uniaxial forces only act in one direction, while biaxial forces act in two different directions. This means that biaxial forces can have a more complex effect on an object, as they can cause both tension and compression in different areas.

## 3. Can biaxial forces be applied simultaneously?

Yes, biaxial forces can be applied at the same time. This is known as biaxial loading, and it can occur in various situations, such as when an object is pulled in two different directions or when it is subjected to pressure from two opposite sides.

## 4. How do biaxial forces affect the strength of materials?

The effect of biaxial forces on the strength of materials depends on the type of material and the direction of the forces. In some cases, biaxial forces can increase the strength of materials, while in others they may cause them to fail at a lower stress level.

## 5. What is the difference between biaxial forces and shear forces?

Biaxial forces act on an object in two different directions, while shear forces act parallel to the surface of an object. Biaxial forces can cause both tension and compression, while shear forces only cause the object to slide or deform.

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