Is My Calculation of Bar Elongation Under Load Correct?

[togo]

I may be doing it correctly, but the number seems way to small for the initial calculation. Plus I am really not sure how to factor in those other forces. Modulus of elasticity E = 114 GPa (if unclear)

thanks

ps. answer is 0.804 mm

 

[Travis_King]

Use consistent units. A Pascal is a N/m^2, so don't use mm, you'll just trip yourself up.

So you've got:
Ao=.0009 m^2
AB=BC=CD=.25 m
E=114 x 10^9 Pa
etc.

As for the other forces, they work in basically the same way, but each force will work on progressively more of the beam. The 80kN will work on the first .25m (as you have worked out), the backwards-acting 40kN will then have .5m to work on, and the 110kN works on the whole thing.

 

[nvn]

Use consistent units. Using mm is a good choice here. I would use N, mm, MPa. Notice, only E and length in post 1 are inconsistent. Below is an example of consistent units, using mm.

80 000 N
Ao = 900 mm^2
AB = BC = CD = 250 mm
E = 114 000 MPa​

(1) By the way, always leave a space between a numeric value and its following unit symbol. E.g., 80 kN, not 80kN. See the international standard for writing units (ISO 31-0). Or see the first image in post 1 for the correct form.

(2) Numbers less than 1 must always have a zero before the decimal point. E.g., 0.25, not .25. See the above links, or any credible textbook.

(3) Also, Pascal is a man, whereas pascal (Pa) is a unit of pressure or stress. Always use correct capitalization and spelling of units.

 

[pongo38]

I would start by drawing the N-diagram. That is, a graph of how the axial force varies from one end to the other.

 

[DeeNos]

Hello,

Thank you for sharing your concerns about the elongation of the bar under load. It is important to ensure that your calculations are accurate and your understanding of the concept is clear.

Firstly, the modulus of elasticity (E) is a measure of a material's stiffness or resistance to deformation. In this case, it is given as 114 GPa, which is a large value indicating a relatively stiff material. This value is often used in engineering calculations to determine the amount of elongation a material will experience under a given load.

To calculate the elongation of the bar, you will need to use the formula:

ΔL = FL/EA

Where ΔL is the change in length, F is the applied force, L is the original length of the bar, and A is the cross-sectional area of the bar.

In order to factor in other forces, such as external loads or supports, you will need to consider them as additional forces acting on the bar and include them in your calculation of F. It is important to carefully consider all forces acting on the bar in order to accurately determine the elongation.

As for the small number you are getting, it is possible that your calculations are correct and the elongation of the bar is indeed 0.804 mm. It is important to remember that even for stiff materials, small amounts of elongation can occur under high loads.

I hope this helps clarify the concept and your calculations. If you have any further questions, please do not hesitate to ask. Keep up the good work in your scientific pursuits!

Best,