### Beam Analysis ProblemFor the beam shown in the figure below:- **Calculate the reaction forces.** - **Express the internal shear force and moment in the beam as functions of \(x\) for \(0 \leq x \leq a\) and \(a \leq x \leq a + b\).**- **Draw the shear and moment diagrams.****Given Parameters:**- \( q_0 = 4 \, \text{kN/m} \) (Triangular distributed load)- \( a = 4 \, \text{m} \)- \( b = 1 \, \text{m} \)- \( F = 5 \, \text{kN} \) (Point load at the end of the beam)**Beam Diagram Description:**The beam rests on two supports. The left support is a fixed end, while the right support is a roller. Over the length \(a\), the beam is subjected to a triangular distributed load beginning from \(q_0\) at the left support and tapering to zero at the right end of \(a\). At the end of length \(a + b\), a point load \(F\) is applied downward.

Calculate the reaction at support A and B due to external loading: ∑FV=0RA+RB=13∑MA=05×5-RB×4+12×4×4×13×4=0RB=8.9167 kNRA=13-8.9167RB=4.0833 kNDraw Shear Force Diagram: equation of shear force interms of x Fx=4.0833-124+4-xx Draw Bending moment diagram: equation of bending moment at a distance x from B Mx=-5x+8.9167×(x-1)-12×x-1×x-123x-1=-5x+8.9167(x-1)-13(x-1)3

Engineering

Civil Engineering

For the beam shown in the figure below • Calculate the reaction forces. • Express the internal shear force and moment in the beam as functions of x for 0 < x < a and a < x< a + b • Draw the shear and moment diagrams q_0 = 4 kN/m a = 4 m b = 1 m F = 5 kN F a b

For the beam shown in the figure below • Calculate the reaction forces. • Express the internal shear force and moment in the beam as functions of x for 0 < x < a and a < x< a + b • Draw the shear and moment diagrams q_0 = 4 kN/m a = 4 m b = 1 m F = 5 kN F a b

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

Bars

In civil engineering, bars refer to steel reinforcement bars or rebars. These are structural members primarily used for reinforcement purposes in masonry works. A bar is characterized by its cross-sectional area, which is negligible compared to its length. Bars are usually manufactured by steel which is uniform throughout the length, or by meshing multiple steel wires. Other materials of the bar include carbon steel, glass fiber, carbon fiber, and basalt fiber. The reinforcing bars are coated with epoxy resins and other materials to enhance some of their properties including corrosion resistance.

Question

### Beam Analysis Problem

For the beam shown in the figure below:

- **Calculate the reaction forces.**

- **Express the internal shear force and moment in the beam as functions of \(x\) for \(0 \leq x \leq a\) and \(a \leq x \leq a + b\).**

- **Draw the shear and moment diagrams.**

**Given Parameters:**

- \( q_0 = 4 \, \text{kN/m} \) (Triangular distributed load)
- \( a = 4 \, \text{m} \)
- \( b = 1 \, \text{m} \)
- \( F = 5 \, \text{kN} \) (Point load at the end of the beam)

**Beam Diagram Description:**

The beam rests on two supports. The left support is a fixed end, while the right support is a roller. Over the length \(a\), the beam is subjected to a triangular distributed load beginning from \(q_0\) at the left support and tapering to zero at the right end of \(a\). At the end of length \(a + b\), a point load \(F\) is applied downward.

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