**Problem Statement**:Given that \( w = 50 \, \text{N/m} \), \( L = 2 \, \text{m} \), and \( P = 150 \, \text{N} \),**a)** Draw the shear force and bending moment diagrams. **b)** Identify the absolute maximum shear force and bending moment in the beam.**Diagram Explanation**:The diagram shows a beam, ABC, subjected to a uniformly distributed load \( w \) and point loads \( P \) at both ends (points A and C). The beam is supported by a roller at point B, placed centrally between A and C. The overall length of the beam between A and C is \( 2L \). Indicated on the beam are:- The evenly distributed downward force \( w \) across the span \( AC \).- The vertical reactions \( P \) at points A and C.**Diagram Details**:- **Supports**: - Point \( A \) is a fixed support. - Point \( B \) is a roller support. - Point \( C \) is a fixed support.- **Loading Configuration**: - Uniform load \( w = 50 \, \text{N/m} \) extends across the entire beam. - Concentrated reactions \( P = 150 \, \text{N} \) are applied at both A and C pointing upwards.- **Dimensions**: - The length between A and B is \( L = 2 \, \text{m} \). - The length between B and C is also \( L = 2 \, \text{m} \). The task involves drawing shear force and bending moment diagrams to calculate maximum internal forces in the beam.

Objective: To draw the shear force and bending moment diagrams and give the values of absolute maximum shear force and bending moment. Given: w = 50 N/m L = 2 P = 150 N The free body diagram of the beam can be drawn as:∑MA=0CW+ →By×2 m+50 N/m×4 m×42 m-150 N×1 m-150 N×4 m=0 →By=150+150×4-50×42 N ⇒By=175 N ∑Fy=0UP+ →Ay-50 N/m×4 m+150 N-175 NBy+150 N=0 →Ay=50×4+175-150-150 N ⇒Ay=75 NThe shear force equations [V(x)] for the beam can be written as: For 0≤x≤1 Vx=75 N-50 N/m×x m=-50x+75 N Linear Vx=0=-50×0+75 N=75 N Vx=1=-50×1+75 N=25 N For 1≤x≤2 Vx=-50x+75 N+150 N=-50x+225 N Vx=1=-50×1+225 N=175 N Vx=2=-50×2+225 N=125 N For 2≤x≤4 Vx=-50x+225 N-175 N=-50x+50 N Vx=2=-50×2+50 N=-50 N Vx=4=-50×4+50 N=-150 N Using the equations and the calculated values, the shear force diagram can be drawn as: The bending moment equations [M(x)] for the beam can be written as: For 0≤x≤1 Mx=75 N×x m-50 N/m×x m×x2 m=-25x2+75x N.m Parabolic Mx=0=-25×02+75×0 N.m=0 Mx=1=-25×12+75×1 N.m=50 N.m For 1≤x≤2 Mx=-25x2+75x N.m+150 N×x-1 m=-25x2+225x-150 N.m [Parabolic] M(x=1)=-25×12+225×1-150 N.m=50 N.m M(x=2)=-25×22+225×2-150 N.m=200 N.m For 2≤x≤4 Mx=-25x2+225x-150 N.m-175 N×x-2 m=-25x2+50x+200 N.m [Parabolic] Mx=2=-25×22+50×2+200 N.m=200 N.m Mx=4=-25×42+50×4+200 N.m=0 Using the equations and the calculated values, the bending moment diagram can be drawn as: From the diagrams, The absolute maximum shear force is: 175 N The absolute maximum bending moment is: 200 N.m .

Answered: Given that w = 50 N/m, L = 2m, and P =…

Engineering

Civil Engineering

Given that w = 50 N/m, L = 2m, and P = 150 N, a) draw the shear force and bending moment diagrams and b) identify the absolute maximum shear force and bending moment in the beam A B. W 이다 p

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

1What is the value of shear at B? 2At what distance from A is zero shear located? 3What is the value of bending moment at C? 4What is the maximum shear stress of the beam? 5What is the maximum bending stress of the beam?
If M = 7.01 and w = 16.8, Determine the Shear Force at point B of the Beam shown.
1) The overhanging beam is loaded as shown in the figure. Draw the shear and bending moment diagrams and determine the maximum bending moment in the beam. A 1m B 20 kN/m 2m TH C 10 kN/m 2m D 1m 40 kN E
The proposed beam shown has a span of 5m. EI = 1 x10^6 kN.m^2 Calculate using Area-Moment method onlyA. Reaction at B B. Moment at A C. Angle of Rotation at B
Draw shear force and bending moment diagram
Calculate the reactions of supports for beam below using forced method of analysis.
From the given figure, what is the force at member BD in kN?
If M = 5.41 and w = 26.4, Determine the Shear Force at point B of the Beam shown. w in kN/m Min kN.m C 3 m A B 4 m
1. Determine the value of EIS under each concentrated load. R₁ 2 m 500 N ↓ 2 m 800 N ↓ 1 m R₂ Use DIM, MAM, SM, & CBM. Draw completely the Shear and Moment Diagrams
Determine the vertical displacement of end B of the cantilevered 6061-T6 aluminum alloy rectangular beam. Consider both shearing and bending strain energy.
I-Shear and Moment Diagram 1. Find the maximum shear and moment values by using the Shear and Moment Diagram. The section of the rectangular beam has a width of 250 mm and a depth of 350 mm. What is the maximum flexural stress of the beam? 15 KN AA RA 2 m B 25 KN 2 m Sk 20 KN/m 2 2 m 4m E 10 KN 2 m RF F
STRUCTURAL ANALYSIS II