### Problem Statement:A rigid beam is supported by bar DE. If the vertical displacement of point D is to be less than 0.1 in., what is the minimum cross-sectional area of bar DE? Assuming that area \(A\), what is the stress state at point \(p\) in the coordinate system shown?### Diagram Details:- The diagram shows a beam \(ABC\) supported by a bar \(DE\).- The beam has two loads of \(800 \, \text{lb}\) acting downward at points \(B\) and \(C\).- Dimensions of the beam: - Length \(AB = 5 \, \text{ft}\) - Length \(BC = 5 \, \text{ft}\) - Point \(A\) is positioned \((0, 0, 5 \, \text{ft})\) - Point \(E\) vertically aligned with \(D\), making line DE perpendicular to AC### Details of Bar \(DE\):- Modulus of Elasticity \(E = 30000 \, \text{ksi}\)- Poisson's Ratio \(\nu = 0.29\)- Distance from \(D\) to \(E\) along the axis: \(12 \, \text{ft}\)### Calculation Requirements:- Minimum cross-sectional area \(A\) in \(\text{in}^2\)- Stress at point \(p\) in the beam### Additional Information:#### Balance Laws:- There is a note referring to balance laws with calculations involving the sums of forces and moments, using the formula: \[ T = \left(\frac{16A}{L^2}\right) = (800)(5) + (800)(5) \]### Calculated Forms:- Stress \(\sigma\) at \(p\) must be computed.- Cross-sectional area \(A\) in \(\text{in}^2\)The calculations must ensure that the displacement constraint at point \(D\) is satisfied with the given parameters and applied loads.

Vertical displacement of point D (∆D) = 0.1 in. Determine the minimum cross sectional area of bar DE…

A rigid beam is supported by bar DE. If the vertical displacement of point D is to be less than 0.1 in, what is the minimum cross-sectional area of bar DE? Assuming that area, what is the stress state at p in the coordinate system shown? A = σ= in² ksi 12 ft AY Ľ₂ Balance Laws 16 ft) 800 lb 5 ft 11 B 800 lb 5 ft Bar DE: E=30000 ksi V = 0.29 point p btc 6 ft E D + (80 (800) (5) +

A rigid beam is supported by bar DE. If the vertical displacement of point D is to be less than 0.1 in, what is the minimum cross-sectional area of bar DE? Assuming that area, what is the stress state at p in the coordinate system shown? A = σ= in² ksi 12 ft AY Ľ₂ Balance Laws 16 ft) 800 lb 5 ft 11 B 800 lb 5 ft Bar DE: E=30000 ksi V = 0.29 point p btc 6 ft E D + (80 (800) (5) +

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Design of structures using FEA

An arrangement, in which various members are interconnected with their constrained relative motion, the whole arrangement is then known as a structure. The degree of freedom of such a structure is zero. In such a structure, the load can act throughout the length of the structure or at the joints.

Question

### Problem Statement:
A rigid beam is supported by bar DE. If the vertical displacement of point D is to be less than 0.1 in., what is the minimum cross-sectional area of bar DE? Assuming that area \(A\), what is the stress state at point \(p\) in the coordinate system shown?

### Diagram Details:
- The diagram shows a beam \(ABC\) supported by a bar \(DE\).
- The beam has two loads of \(800 \, \text{lb}\) acting downward at points \(B\) and \(C\).
- Dimensions of the beam:
- Length \(AB = 5 \, \text{ft}\)
- Length \(BC = 5 \, \text{ft}\)
- Point \(A\) is positioned \((0, 0, 5 \, \text{ft})\)
- Point \(E\) vertically aligned with \(D\), making line DE perpendicular to AC

### Details of Bar \(DE\):
- Modulus of Elasticity \(E = 30000 \, \text{ksi}\)
- Poisson's Ratio \(\nu = 0.29\)
- Distance from \(D\) to \(E\) along the axis: \(12 \, \text{ft}\)

### Calculation Requirements:
- Minimum cross-sectional area \(A\) in \(\text{in}^2\)
- Stress at point \(p\) in the beam

### Additional Information:
#### Balance Laws:
- There is a note referring to balance laws with calculations involving the sums of forces and moments, using the formula:
\[
T = \left(\frac{16A}{L^2}\right) = (800)(5) + (800)(5)
\]

### Calculated Forms:
- Stress \(\sigma\) at \(p\) must be computed.
- Cross-sectional area \(A\) in \(\text{in}^2\)

The calculations must ensure that the displacement constraint at point \(D\) is satisfied with the given parameters and applied loads.

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