### Structural Analysis of BeamIn this lesson, we will analyze a simply supported beam subjected to various loads. We will draw and label the shear force (V) and bending moment (M) diagrams, filling in the blanks for shear forces and bending moments, and find the maximum moments as well as determine the equations governing the shear force (V), and bending moment (M) in specific regions.#### Beam Diagram- A simply supported beam AB of length 22 meters- A roller support at point A and a pin support at point B- The beam is subjected to a point load of 6 kN at 3 meters from support A- An angled point load of 15 kN acting at 20 degrees to the horizontal acting 14 meters from support A.#### Support Reactions- Reaction forces calculated at support A (Ay) and support B (By) - \( Ay = 19.29 \, \text{kN} \) - \( By = 22.71 \, \text{kN} \)#### Shear Force (V) DiagramThe shear force diagram shows the variation of the shear force along the length of the beam. The shear force at any section is the algebraic sum of all vertical forces either to the left or right of the section.1. Start at A with \( V = 19.29 \, \text{kN} \) (upward reaction)2. At 3 meters from A, decrease by 6 kN (due to a downward point load) - \( V = 19.29 - 6 = 13.29 \, \text{kN} \)3. At B, shear force drops to \( -22.71 \, \text{kN} \).#### Bending Moment (M) DiagramThe bending moment diagram indicates the bending effect (moment) of the forces acting on the beam:1. The moment along the beam changes based on the moments induced by the external loads and support reactions.2. The bending moment equation \( M_{(x)} \) will be applicable in the region 3 meters < \( x \) < 12 meters.#### Fill in the Blanks- Shear Force, \( V_{(3 < x < 12)} \): - Bending Moment, \( M_{(3 < x < 12)} \): - Maximum Bending Moment,

The beam is an important element in the construction of any structure or building. It resists…

Answered: Draw and label theV and M 15KN…

Draw and label theV and M 15KN diagrams. Fill in the blanks. Find M- max and the equations for q. V, and M in the region 3x<12. Ag 1131 kN ++ 34×-は Begun Vegu= Magn= V=D@ x= Mux= 3

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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### Structural Analysis of Beam

In this lesson, we will analyze a simply supported beam subjected to various loads. We will draw and label the shear force (V) and bending moment (M) diagrams, filling in the blanks for shear forces and bending moments, and find the maximum moments as well as determine the equations governing the shear force (V), and bending moment (M) in specific regions.

#### Beam Diagram

- A simply supported beam AB of length 22 meters
- A roller support at point A and a pin support at point B
- The beam is subjected to a point load of 6 kN at 3 meters from support A
- An angled point load of 15 kN acting at 20 degrees to the horizontal acting 14 meters from support A.

#### Support Reactions

- Reaction forces calculated at support A (Ay) and support B (By)
- \( Ay = 19.29 \, \text{kN} \)
- \( By = 22.71 \, \text{kN} \)

#### Shear Force (V) Diagram

The shear force diagram shows the variation of the shear force along the length of the beam. The shear force at any section is the algebraic sum of all vertical forces either to the left or right of the section.

1. Start at A with \( V = 19.29 \, \text{kN} \) (upward reaction)
2. At 3 meters from A, decrease by 6 kN (due to a downward point load)
- \( V = 19.29 - 6 = 13.29 \, \text{kN} \)
3. At B, shear force drops to \( -22.71 \, \text{kN} \).

#### Bending Moment (M) Diagram

The bending moment diagram indicates the bending effect (moment) of the forces acting on the beam:

1. The moment along the beam changes based on the moments induced by the external loads and support reactions.
2. The bending moment equation \( M_{(x)} \) will be applicable in the region 3 meters < \( x \) < 12 meters.

#### Fill in the Blanks

- Shear Force, \( V_{(3 < x < 12)} \):

- Bending Moment, \( M_{(3 < x < 12)} \):

- Maximum Bending Moment,

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