### Problem Statement:When the two forces are placed on the beam, the diameter of the steel rod (E=200 GPa) BC decreases from 40 mm to 39.99 mm. Calculate the magnitude of each force P.### Diagram Explanation:The diagram provided shows a beam setup with the following details:- A beam is fixed at point A and rests on a roller support at point B.- The beam extends horizontally from point A to point B, which is a distance of 2 meters.- Forces, labeled as P, are applied vertically downwards at two points between A and B, each spaced 1 meter apart.- An inclined steel rod, labeled BC, is attached from point B to point C. - The rod BC has a length of 1 meter vertically and 0.75 meters horizontally. ### Parameters:- Modulus of Elasticity (E) for steel rod BC = 200 GPa.- Original diameter of steel rod BC = 40 mm.- Diameter of steel rod BC after the forces are applied = 39.99 mm. ### Objective:Calculate the magnitude of each force P.

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When the two forces are placed on the beam, the diameter of the steel rod (E-200GPa) BC decreases from 40 mm to 39.99 mm. Calculate the magnitude of each force P.

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

Matrix Algebra for Structural analysis

Structural analysis is a process in which the effects of different loads and internal forces, acting on structures and their elements are determined. This method of analysis is effective in detecting the failure loads of the structural elements and the design can be altered before commencing the construction process, which ensures proper strength and safety of the structures.

Question

### Problem Statement:

When the two forces are placed on the beam, the diameter of the steel rod (E=200 GPa) BC decreases from 40 mm to 39.99 mm. Calculate the magnitude of each force P.

### Diagram Explanation:

The diagram provided shows a beam setup with the following details:
- A beam is fixed at point A and rests on a roller support at point B.
- The beam extends horizontally from point A to point B, which is a distance of 2 meters.
- Forces, labeled as P, are applied vertically downwards at two points between A and B, each spaced 1 meter apart.
- An inclined steel rod, labeled BC, is attached from point B to point C.
- The rod BC has a length of 1 meter vertically and 0.75 meters horizontally.

### Parameters:
- Modulus of Elasticity (E) for steel rod BC = 200 GPa.
- Original diameter of steel rod BC = 40 mm.
- Diameter of steel rod BC after the forces are applied = 39.99 mm.

### Objective:
Calculate the magnitude of each force P.

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