Question

An Elastic, linear, wedge-shaped thin plate ABC is fixed along line BC and loaded with a concentrated Moment A above point A as shown in the figure. Assume known Elastic constants $E, \nu$, and neglect body forces. (Own weight). A. Write the appropriate boundary condition for the given case. (according to the Saint Venant's Principle) B. Found the appropriate stress field using the Airy function: $\phi = A + B(\sin2\alpha - 2\alpha \cos2\alpha)/[2(\sin2\alpha - 2\alpha \cos2\alpha)]$ A,B - constants. The boundary conditions are to be written in a \"compact\" form such as: $\sigma_\theta (r, \alpha) = 0$ $\tau_{r\theta} (r, \alpha) = 0$

          An Elastic, linear, wedge-shaped thin plate ABC is fixed along line BC and loaded with
a concentrated Moment A above point A as shown in the figure.
Assume known Elastic constants $E, \nu$, and neglect body forces. (Own weight).
A. Write the appropriate boundary condition for the given case. (according to the
Saint Venant's Principle*)
B. Found the appropriate stress field using the Airy function:
$\phi = A + B(\sin2\alpha - 2\alpha \cos2\alpha)/[2(\sin2\alpha - 2\alpha \cos2\alpha)]$
A,B - constants.
*The boundary conditions are to be written in a \"compact\" form such as:
$\sigma_\theta (r, \alpha) = 0$
$\tau_{r\theta} (r, \alpha) = 0$

Show more…

An Elastic, linear, wedge-shaped thin plate ABC is fixed along line BC and loaded with
a concentrated Moment A above point A as shown in the figure.
Assume known Elastic constants E, ν, and neglect body forces. (Own weight).
A. Write the appropriate boundary condition for the given case. (according to the
Saint Venant's Principle*)
B. Found the appropriate stress field using the Airy function:
ϕ = A + B(sin2α - 2αcos2α)/[2(sin2α - 2αcos2α)]
A,B - constants.
*The boundary conditions are to be written in a c̈ompactf̈orm such as:
σθ (r, α) = 0
τrθ (r, α) = 0

Added by Andrea G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Dharmendra Maheshwari

Step 1

The appropriate boundary condition for this case, according to Saint Venant's Principle, is that the stress and strain fields should decay rapidly away from the loaded region. This means that at the fixed boundary line BC, the stress and strain should approach Show more…

Show all steps

lock

Thanks for your feedback!

Hi, Here's a question similar to this one: https://www.chegg.com/homework-help/assume-moment-m-acts-plane-vertex-wedge-cantilever-shown-fig-chapter-3-problem-29p-solution-9780137080144-exc But the boundary conditions aren't cited. I'd like to know specifically what the right approach is for determining the boundary conditions in this type of question - especially in cases of concentrated Moments and cylindrical coordinates. Thanks! An elastic, linear, wedge-shaped thin plate ABC is fixed along line BC and loaded with a concentrated Moment A above point A as shown in the figure. Assume known elastic constants E, x, and neglect body forces (own weight). A. Write the appropriate boundary condition for the given case (according to the Saint Venant's Principle*). B. Find the appropriate stress field using the Airy function: Î¦ = A + B(SIN^2Î¸ - 2 COS^2Î¸)/[2(SIN^2Î¸ - 2 COS^2Î¸)], where A and B are constants. *The boundary conditions are to be written in a "compact" form such as: 0 = xÎ±M + r - Î± = 0

Play audio

Feedback

Powered by NumerAI

Dharmendra Maheshwari and 99 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later