Finding the max. deflection of the beam

[farry1024]

For the Electronic Bathroom Scale. The maximum load on a
beam is assumed to be 75kg.

(a) Find the max. deflection by using the Young’s Modulus
E=200,000 N/mm². Is it small? Also see next page for the
dimensions of the beam. Hint: For small deflection, tan phyter » phyter.
Use the given Excel template file if needs.

(b) Determine the relationship of the applied load (say, mass in kg
here!) against the beam surface strain (e). Hint: Using Excel to
calculate the Bending Moment at the surfaces of the beam first.
Then use the equation (M/I)(h/2) = Ee.

(c) What have you observed?

What formula should I use the find the max. deflection?

 

[nvn]

Hi, farry1024. The PF rules state we are not allowed to tell you how to approach or solve your homework problem. See the required homework template when you start to create a new thread in the homework forums. You must list relevant equations yourself, and show your work; and then someone might check your math.

 

[Mene]

(a) To find the maximum deflection, we can use the formula d = (FL^3)/(3EI), where d is the deflection, F is the maximum load, L is the length of the beam, E is the Young's Modulus, and I is the moment of inertia. In this case, F = 75kg, L = the length as provided in the dimensions of the beam, and E = 200,000 N/mm². Using the given Excel template, we can calculate the moment of inertia (I) of the beam. Then, we can plug in these values to calculate the maximum deflection.

Based on the given information, the maximum deflection is likely to be small as the Young's Modulus is relatively high and the maximum load is only 75kg. We can also confirm this by comparing the deflection to the length of the beam. If the deflection is significantly smaller than the length of the beam, it can be considered small.

(b) The relationship between the applied load and the beam surface strain can be determined by using the formula M = (EI/h)(e), where M is the bending moment, E is the Young's Modulus, I is the moment of inertia, h is the height of the beam, and e is the strain. By calculating the bending moment at the surfaces of the beam using the given Excel template, we can then use this equation to determine the strain at the beam surface. We can then plot a graph of applied load (in kg) against beam surface strain to observe the relationship.

(c) From the calculations and graph, we can observe that there is a linear relationship between the applied load (mass) and the beam surface strain. As the load increases, the strain also increases proportionally. This relationship can be described by the equation M = (EI/h)(e), where the bending moment (M) is directly proportional to the applied load (F) and the strain (e) is directly proportional to the bending moment. This relationship can also be confirmed by the graph, where the slope represents the Young's Modulus (E/h), which is constant for a given material.