Solid Mechanics Beam Stress Question

  • #1
Leighanne
2
0
Homework Statement
Looking for some help in solving this practice problem, I have tried multiple times and can't seem to get to the correct answers.
Relevant Equations
The solid 30 mm diameter steel [E = 200 GPa] shaft shown in Figure supports two pulleys. For the loading shown, use discontinuity functions to compute:

(a) the deflection of the shaft at pulley B.

(b) the deflection of the shaft at pulley C.

answers: (1.539mm, 6.15mm)
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  • #2
You are supposed to use the singularity function to find the deflections. You need to write the moment as a function of ##x##. Then the deflections come from integrating twice:

$$EI \frac{d^2y}{dx^2} = M(x)$$

Why are you trying to find the shear stress?
 
  • #3
Uploaded the wrong solution attempt whoops!
heres the correct one.
1704650460080.png
 
  • #4
Leighanne said:
Uploaded the wrong solution attempt whoops!
heres the correct one.
View attachment 338230
There should be a constant moment that you have not included in ##M(x)##. There may be more, but start there( i.e there is vertical reaction and moment at A under equilibrium).
 

1. How do you calculate the stress in a beam?

To calculate the stress in a beam, you can use the formula: Stress = Force / Area. This means you divide the force acting on the beam by the cross-sectional area of the beam.

2. What are the different types of stress that can occur in a beam?

The different types of stress that can occur in a beam are tensile stress (stretching), compressive stress (squeezing), and shear stress (sliding).

3. How does the material properties of a beam affect its stress levels?

The material properties of a beam, such as its Young's Modulus and yield strength, directly affect its stress levels. Beams made of materials with higher Young's Modulus and yield strength can withstand higher stress levels before failing.

4. What is the difference between normal stress and shear stress in a beam?

Normal stress acts perpendicular to the surface of the beam, either in tension or compression, while shear stress acts parallel to the surface of the beam, causing it to slide or deform.

5. How can I determine if a beam will fail under a given load?

You can determine if a beam will fail under a given load by calculating the maximum stress the beam will experience and comparing it to the beam's yield strength. If the maximum stress exceeds the yield strength, the beam will fail.

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