- #1
How do I calculate radial stress in a u-shaped t-beam with varying thickness?
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SUMMARY
The discussion focuses on calculating radial stress (\(\sigma_{r}\)) in a u-shaped t-beam with varying thickness, specifically at \(\theta=0\) degrees. The formula provided is \(\sigma_{r}=\frac{1}{tr}\int t\sigma_{\theta}dr\), where the integration limits are defined by the inner radius \(a\) and a variable radius \(r\). The user struggles with incorporating the varying thickness into the integration process and seeks clarification on defining the limits for the integral. The proposed methods involving subscripts for different cross-section portions do not yield satisfactory results.
PREREQUISITES- Understanding of radial stress calculations in structural engineering
- Familiarity with integration techniques in calculus
- Knowledge of beam theory and cross-sectional analysis
- Experience with variable thickness in mechanical components
- Research "Integration techniques for varying thickness in beams"
- Study "Radial stress calculations in cylindrical structures"
- Learn about "Finite Element Analysis (FEA) for complex geometries"
- Explore "Beam theory applications in mechanical engineering"
Structural engineers, mechanical engineers, and students involved in beam analysis and stress calculations will benefit from this discussion.
- #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...?