- #1
How do I calculate radial stress in a u-shaped t-beam with varying thickness?
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Discussion Overview
The discussion centers around calculating radial stress in a u-shaped t-beam with varying thickness, specifically at \(\theta=0\) degrees. Participants are exploring the integration process required to account for the varying thickness of the cross-section in their calculations.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant expresses uncertainty about how to treat the varying thickness of the cross-section when integrating with respect to radius.
- Another participant requests to see the original calculations to identify potential errors in the approach.
- A participant presents a formula for radial stress, \(\sigma_{r}=\frac{1}{tr}\int t\sigma_{\theta}dr\), and questions the inclusion of thickness in the equation, suggesting it cancels out.
- Further elaboration is provided with attempts to define the limits of integration for different sections of the beam, indicating confusion over how to apply the varying thickness in the calculations.
- One participant mentions plotting radial stress as a function of radius, indicating an interest in visualizing the results.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on how to handle the varying thickness in their calculations, and multiple competing views on the integration approach remain unresolved.
Contextual Notes
There are limitations regarding the assumptions made about the thickness and its effect on the integration process, as well as the definitions of the limits of integration that remain unclear.
- #2
Pyrrhus
Homework Helper
- 2,180
- 0
Hey Johnny,
You have to show your work first, so we can pinpoint where you went wrong.
You have to show your work first, so we can pinpoint where you went wrong.
- #3
Jonny Black
- 4
- 0
\sigma_{r}=\frac{1}{tr}\int t\sigma_{\theta}dr
with a lower limit of a=inner radius, and upper limit of r=variable radius. For one, why is the thickness even included in the equation since it cancels anyway, and two, how do I treat the varying thickness of the cross-section? I have tried
\sigma_{r}=\frac{1}{t_{1}r}\int^{b}_{a} t_{1}\sigma_{\theta}dr+\frac{1}{t_{2}r}\int^{c}_{b} t_{2}\sigma_{\theta}dr
\sigma_{r}=\frac{1}{t_{1}r}\int^{r}_{a} t_{1}\sigma_{\theta}dr+\frac{1}{t_{2}r}\int^{r}_{b} t_{2}\sigma_{\theta}dr
where the subscripts 1 & 2 denote the horizontal and vertical portions of the cross-section, respectively. Neither method gives viable results. a, b, and c denote radius's at each definition of the cross-section starting with the inner radius. I have found \sigma_{\theta} already, I just need to know how to define the limits of the integral
with a lower limit of a=inner radius, and upper limit of r=variable radius. For one, why is the thickness even included in the equation since it cancels anyway, and two, how do I treat the varying thickness of the cross-section? I have tried
\sigma_{r}=\frac{1}{t_{1}r}\int^{b}_{a} t_{1}\sigma_{\theta}dr+\frac{1}{t_{2}r}\int^{c}_{b} t_{2}\sigma_{\theta}dr
\sigma_{r}=\frac{1}{t_{1}r}\int^{r}_{a} t_{1}\sigma_{\theta}dr+\frac{1}{t_{2}r}\int^{r}_{b} t_{2}\sigma_{\theta}dr
where the subscripts 1 & 2 denote the horizontal and vertical portions of the cross-section, respectively. Neither method gives viable results. a, b, and c denote radius's at each definition of the cross-section starting with the inner radius. I have found \sigma_{\theta} already, I just need to know how to define the limits of the integral
- #4
- #5
Jonny Black
- 4
- 0
...Anybody...?