a) If olow 160 MPa, select the most economical metric wide- flange shape that should be used to support the loads shown, b) calculate the Von Mises equivalent stress at point Q (top of beam's cross-section), c) calculate the Von Mises equivalent stress at point P (junction between flange and web), d) are points P and Q safe based on o? allow 40 kN 2.2 kN/m Wide-flange shape (metric) 4.5 m 2.7 m

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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### Problem Statement:

Given:
- Allowable stress, \(\sigma_{allow} = 160 \, \text{MPa}\)

Tasks:
a) Select the most economical metric wide-flange shape that should be used to support the loads shown.
b) Calculate the Von Mises equivalent stress at point \(Q\) (top of beam’s cross-section).
c) Calculate the Von Mises equivalent stress at point \(P\) (junction between flange and web).
d) Determine if points \(P\) and \(Q\) are safe based on \(\sigma_{allow}\).

### Diagram Explanation:

#### Beam Setup:
- The beam is horizontally positioned.
- Supports are indicated at points \(A\) and \(C\).
- There is a concentrated load of \(40 \, \text{kN}\) acting vertically downward at the midpoint between \(A\) and \(C\).
- A distributed load of \(2.2 \, \text{kN/m}\) extends from \(A\) to \(C\).

#### Dimensional Details:
- Distance from \(A\) to \(B\) is \(4.5 \, \text{m}\).
- Distance from \(B\) to \(C\) is \(2.7 \, \text{m}\).

#### Cross-Section Details:
- The cross-section is depicted as a wide-flange shape (typical metric I-beam).
- Point \(Q\) is at the top of the beam’s cross-section.
- Point \(P\) is at the junction between the flange and the web.

### Analysis Requirement:
Acquire the necessary stress calculations and ensure design safety by comparing equivalent stresses at key structural points against the given allowable stress.
Transcribed Image Text:### Problem Statement: Given: - Allowable stress, \(\sigma_{allow} = 160 \, \text{MPa}\) Tasks: a) Select the most economical metric wide-flange shape that should be used to support the loads shown. b) Calculate the Von Mises equivalent stress at point \(Q\) (top of beam’s cross-section). c) Calculate the Von Mises equivalent stress at point \(P\) (junction between flange and web). d) Determine if points \(P\) and \(Q\) are safe based on \(\sigma_{allow}\). ### Diagram Explanation: #### Beam Setup: - The beam is horizontally positioned. - Supports are indicated at points \(A\) and \(C\). - There is a concentrated load of \(40 \, \text{kN}\) acting vertically downward at the midpoint between \(A\) and \(C\). - A distributed load of \(2.2 \, \text{kN/m}\) extends from \(A\) to \(C\). #### Dimensional Details: - Distance from \(A\) to \(B\) is \(4.5 \, \text{m}\). - Distance from \(B\) to \(C\) is \(2.7 \, \text{m}\). #### Cross-Section Details: - The cross-section is depicted as a wide-flange shape (typical metric I-beam). - Point \(Q\) is at the top of the beam’s cross-section. - Point \(P\) is at the junction between the flange and the web. ### Analysis Requirement: Acquire the necessary stress calculations and ensure design safety by comparing equivalent stresses at key structural points against the given allowable stress.
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