How Do You Calculate Wheatstone Bridge Output for Axial Strain Gauges?

[loobloke]

Homework Statement

A strip of high-strength steel has a length of 30 cm and a cross section of 1 mm by 20 mm. The modulus of elasticity is 200 GPa, and Poission's ratio is 0.25. It is subjected to an axial load of 15,000N. It is instrumented with two axial strain gauges with R=159Ω and a gauge factor of 2.02. These two gauges are connected into opposite legs of a Wheatstone bridge (R1 and R3). The two fixed resistors are also 159Ω, and the supply voltage is 3.4V. The bridge is adjusted to zero-voltage output before the load is applied.
Find the output of the bridge with the load applied.

Homework Equations

Hooke's Law
Wheatstone Bridge Equation for Strain

The Attempt at a Solution

I've used the cross sectional area and Hooke's Law to find the strain. From then I just sub it into the wheatstone bridge equation?

However extra information is given so I'm afraid I might be missing something out.
We are applying axial load and measuring axial strain so possion's ratio is irrelevant. Likewise the length of the beam is also irrelevant then. Am I correct in thinking this?

Thanks.

 

[KataKoniK]

Thank you for your post. You are correct in your thinking that the Poisson's ratio and length of the beam are irrelevant in this problem, as we are only concerned with the axial strain and load on the beam. Your approach of using Hooke's Law and the Wheatstone Bridge equation is a good start. However, there are a few additional steps that you may want to consider in order to find the output of the bridge with the load applied.

First, it may be helpful to draw a diagram of the Wheatstone Bridge and label the resistors and gauges. This can help you visualize the circuit and make sure you are using the correct values in your calculations.

Next, you will need to find the change in resistance for each gauge due to the applied load. This can be done using the gauge factor and the initial resistance values. Once you have the change in resistance for each gauge, you can use the Wheatstone Bridge equation to find the output of the bridge with the load applied. Remember to use the adjusted resistance values for R1 and R3, as the initial zero-voltage output means that the bridge has been balanced.

I hope this helps guide you towards finding the correct solution. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!