Combining Errors for Stress Calculation

In summary, the conversation discusses computing the standard error of a stress related calculation. The formulas for common combinations of errors are presented and the individual's equation is analyzed. There is confusion about whether the working to compute the standard error is correct.
  • #1
charlesltl
5
0
Hello Everyone,

I am trying to compute the standard error of a stress related calculation.

Let's consider the following:

A [itex]\pm[/itex] [itex]\Delta[/itex]A
B [itex]\pm[/itex] [itex]\Delta[/itex]B

where A and B are the mean values while [itex]\Delta[/itex]A and [itex]\Delta[/itex]B are the respective standard errors.

The common combination of errors formulas are as follows:

y = A + B then, [itex]\Delta[/itex]y = √([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2)

y = k. A then, [itex]\Delta[/itex]y = k.[itex]\Delta[/itex]A

Now my equation is,

y = k2 . [ A + k1 . ( A + B + C ) ]

May I know if my following working is correct?

( A + B + C )
= √([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2 + [itex]\Delta[/itex]C2)

k1 . ( A + B + C )
= k1 . √([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2 + [itex]\Delta[/itex]C2)

A + k1 . ( A + B + C )
= √[[itex]\Delta[/itex]A2 + (k1 . √([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2 + [itex]\Delta[/itex]C2))2]
= √[[itex]\Delta[/itex]A2 + k12 . ([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2 + [itex]\Delta[/itex]C2)]

k2 . [ A + k1 . ( A + B + C ) ]
= k2 . √[[itex]\Delta[/itex]A2 + k12 . ([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2 + [itex]\Delta[/itex]C2)]


I am confused because I was suggested that it should be,
k2 . [ A + k1 . ( A + B + C ) ]
= k2 . √ [k1. [itex]\Delta[/itex]A2 + k12 . ([itex]\Delta[/itex]A2+[itex]\Delta[/itex]B2 + [itex]\Delta[/itex]C2)]

Your input in highly appreciated.

Charles
 
Mathematics news on Phys.org
  • #2
That last appears to be the "mean square error" rather than the "error".
 
  • #3
Would you suggest that my working to compute the standard error is correct?
 

Related to Combining Errors for Stress Calculation

What is "Combining Errors for Stress Calculation"?

"Combining Errors for Stress Calculation" refers to the process of combining multiple sources of error or uncertainty in order to calculate the overall stress on a material or structure. This is an important concept in engineering and materials science, as it allows for a more accurate understanding of the potential failure of a material.

Why is it important to consider combining errors for stress calculation?

Considering combining errors for stress calculation is important because it allows for a more comprehensive and accurate analysis of the potential failure of a material or structure. By taking into account all sources of error, engineers and scientists can make more informed decisions about the safety and reliability of their designs.

What are some common sources of error in stress calculations?

Some common sources of error in stress calculations include measurement errors, material variability, and modeling assumptions. Measurement errors can occur due to limitations in equipment or human error. Material variability refers to natural variations in the properties of a material, such as density or strength. Modeling assumptions can also introduce errors, as the real-world behavior of materials can be complex and difficult to accurately simulate.

How are errors in stress calculations typically combined?

Errors in stress calculations are typically combined using statistical methods, such as the root sum square (RSS) method. This involves taking the square root of the sum of the squares of each individual error. This approach is based on the assumption that the errors are independent and normally distributed.

Are there any limitations or drawbacks to combining errors for stress calculation?

Yes, there are limitations and drawbacks to combining errors for stress calculation. One limitation is that it assumes errors are independent and normally distributed, which may not always be the case. Additionally, combining errors can only provide an estimate of the overall uncertainty and may not accurately capture all sources of error. It is also important to note that combining errors does not eliminate them entirely, but rather provides a more comprehensive understanding of their impact on stress calculations.

Similar threads

I Two-Mass Oscillator: Plotting Amplitudes Over Frequencies in Hertz
    • Mechanics
Replies
5
Views
387
A Advice needed for exposure time computation for galaxies
    • Astronomy and Astrophysics
Replies
2
Views
1K
Wrong solution order using Runge Kutta 4
    • Programming and Computer Science
Replies
15
Views
2K
Is My Calculation for Standard Error of a Stress Calculation Correct?
    • Introductory Physics Homework Help
Replies
5
Views
2K
Oven controller block diagram, transfer function and temperature calcs
    • Engineering and Comp Sci Homework Help
Replies
24
Views
2K
A Monte Carlo Wang-Landau_antiferromagnetic perovskite
    • Atomic and Condensed Matter
Replies
3
Views
930
How Does Inserting Different Dielectric Materials Affect Capacitor Performance?
    • Introductory Physics Homework Help
Replies
9
Views
2K
MHB Plotting the error vs the change in 1/dx
    • General Math
Replies
1
Views
1K
I Error propagation of a variable for an integral
    • General Math
Replies
6
Views
3K
Comp Sci An Introduction to Deep Learning and Modifying Code
    • Engineering and Comp Sci Homework Help
Replies
7
Views
911

Hot Threads

Recent Insights

Back
Top