What Is the Correct Calculation of Stress in Welded Cylindrical Rods AB and BC?

In summary, average normal stress, also known as tensile stress, is a measure of the internal resistance of a material to external forces. It is calculated by dividing the applied force by the cross-sectional area of the material and is influenced by factors such as the applied force, material properties, and shape/size of the material. This type of stress differs from shear stress, which causes materials to deform or slide. Understanding average normal stress is important in fields such as engineering, physics, and materials science, as well as in everyday situations such as lifting objects or walking on a surface.
  • #1
freespirit
8
0
Two solid cylinderical rods AB & BC are welded together at B & loaded as shown. Knowing that d(1)=30mm & d(2)=50mm, find the average normal stress in the midsection of (a)rod AB, (b) rod BC.
B____________C
125kN--->| |
A______________| |
60kN<---| | |
| | |
|______________| |
|<- 0.9m------>| |
125kN--->|____________|
|<---1.2m--->|


stress = P/A

(a) A= pie r ^2=pie (30mm/2)^2=.000707 m^2
stress=P/A= (60x10^3 N)/(.000707)=84.9MPa

(b) A= pie r^2)= pie(50mm/2)^2=.001963
stress= P/A= (250x10^3)/.001963=106.1 MPa

the stress for (b) is wrong; it's suppose to be 96.8MPa Can someone show me what I have done wrong and explain why it should be done differently? Thanks
 
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  • #2
figure for post

......B____________C
.....125kN--->| ...|
...A______________|... |
60kN<---|.... | ...|
...| ....| ...|
...|______________|... |
...|<- 0.9m------>|... |
.....125kN--->|___________|
......|<---1.2m-->|
 
  • #3
figure for post

I can't seem to get the figure to turn out right sorry about this, I will attempt to explain it in words.

the first rod AB is 0.9m long and has a diameter of d1=(30mm); 60kN<---- from the A end of this rod the second rod BC attaches to the B end of the first rod it is 1.2m long and has a diameter is d2=(50mm); 125 kN is applied both above and below where it is attached to the first rod on the B end 125kN---->
 
  • #4
Maybe I just have a short attention span, but I don't see the situation. I've got rod AB welded to BC (connected at B, naturally). A is on the lefthand side and C is on the righthand side of my scrap paper. Tell me the following and I'll try to help you:

- Force applied at point A and the direction the force is pointing.

- Force applied at point B (and the direction).

- Force applied at point C (and the direction).

- Whether or not the rods are attached to anything (e.g. mechanical ground) and how.
 
  • #5
forces

force at A is pointed to the left and is in the center on the end
force at B is pointed to the right and is at the top and bottom of where C attaches. Can I send you a pic of the thing? It keeps telling me here that the attachment is bigger then 400X 400 and i made sure it wasn't
 
  • #6
OK, I think I get it. The way you're describing it is a little difficult to follow and may be the reason you're having trouble solving it.

In cheesy ASCII art, here's my sketch (sans dimensions):

Code: 
        125kN    __________
            --->|          |/
          ______|          |/
         |      |          |/
60kN  <--|      |          |/
         |______|          |/
                |          |/
            --->|__________|/
          125kN  

         A      B          C

So you've got A B and C going from left to right. At surface C, the bar is up against a wall (for all intents and purposes, connected to mechanical ground). At surface A, there is a force of 60 kN to the left. At surface B, there are two points of loading, each with 125 kN, as sketched.

Member AB is in tension. Since the loading is 60 kN and the area is as you have computed, the normal stress is ~84.9 MPa, as you calculated.

Member BC is in compression. The compressive force is (125+125-60)kN = 190 kN. (There is a reaction force normal to the wall that balances this force). The normal stress is again given by &sigma; = P/A. Use the proper value for P with the area you computed and you will find the answer.
 

1. What is average normal stress?

Average normal stress, also known as tensile stress, is the force per unit area that is applied perpendicular to a surface. It is a measure of the internal resistance of a material to external forces.

2. How is average normal stress calculated?

Average normal stress is calculated by dividing the applied force by the cross-sectional area of the material that is experiencing the force. The unit of measurement for average normal stress is typically in units of Pascals (Pa).

3. What factors affect average normal stress?

The magnitude of average normal stress is influenced by the amount and direction of the applied force, as well as the material properties such as its elasticity and strength. Additionally, the shape and size of the material can also impact the distribution of stress.

4. How does average normal stress differ from shear stress?

While average normal stress is a measure of the force applied perpendicular to a surface, shear stress is a measure of the force applied parallel to a surface. Average normal stress causes a material to elongate or compress, while shear stress causes a material to deform or slide.

5. What are the practical applications of understanding average normal stress?

Understanding average normal stress is important in the design and construction of structures and machines, as it helps determine the strength and durability of materials. It is also relevant in fields such as engineering, physics, and materials science, as well as in everyday situations such as lifting objects or walking on a surface.

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