There are two distributed loads acting on the beam, left and right. Replace them with equivalent concentrated loadsrespectively:1. The distributed load on the left part of the beam is equivalent to F₁:Magnitude of it: F₁ =N;Oo Location of it: x₁ =m to the right of A;2. The distributed load on the right part of the beam is equivalent to F2:o Magnitude of it: F₂ =N;o Location of it: x₂ =. The two supports are replaced by corresponding reactions:1. Reactions on A:2. Reactions on B:• Equilibrium equations:1. EFx = 0: Ax =2. EMA = 0: By =3. EMB= 0: Ay==;N;→m to the right of A;N; For a = 1.5m, determine the reactions at pin A and roller B.1800 N/mA4 mSolution:• There are two distributed loads acting on the beam, left and right. Replace them with equivalent concentrated loadsrespectively:1. The distributed load on the left part of the beam is equivalent to F₁:o Magnitude of it: F₁ =N;o Location of it: x₁ =m to the right of A;2. The distributed load on the right part of the beam is equivalent to F2:o Magnitude of it: F2 =N;o Location of it: X₂ =600 N/mB1. Reactions on A:2 Reactions on R• The two supports are replaced by corresponding reactions:→m to the right of A;

Answered: Image /qna-images/answer/bcdc955f-21ec-4739-b48a-32bacc209893.jpg

For a = 1.5m, determine the reactions at pin A and roller B. 1800 N/m A 4 m Solution: • There are two distributed loads acting on the beam, left and right. Replace them with equivalent concentrated loads respectively: 1. The distributed load on the left part of the beam is equivalent to F₁: o Magnitude of it: F₁ = N; o Location of it: x₁ = m to the right of A; 2. The distributed load on the right part of the beam is equivalent to F2: o Magnitude of it: F2 = N; o Location of it: X₂ = 600 N/m B 1. Reactions on A: 2 Reactions on R • The two supports are replaced by corresponding reactions: → m to the right of A;

For a = 1.5m, determine the reactions at pin A and roller B. 1800 N/m A 4 m Solution: • There are two distributed loads acting on the beam, left and right. Replace them with equivalent concentrated loads respectively: 1. The distributed load on the left part of the beam is equivalent to F₁: o Magnitude of it: F₁ = N; o Location of it: x₁ = m to the right of A; 2. The distributed load on the right part of the beam is equivalent to F2: o Magnitude of it: F2 = N; o Location of it: X₂ = 600 N/m B 1. Reactions on A: 2 Reactions on R • The two supports are replaced by corresponding reactions: → m to the right of A;

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

A rectangular beam is supported at both ends. It carries two concentrated load of 190KN, a clockwise moment of 160KN- m, and a uniformly distributed load "w". The modulus of elasticity of the beam is 150GPA. Solve the following if the reaction at point B is 309.63888888889KN, upward. USE ANY МЕТНOD BEAM DIMENSION: Width = 130mm , %3D Height = 460mm %3D NOTE: b = 4.2m ; Also, DON'T FORGET TO TYPE DOWN THE CORRECT UNITS (IF NEEDED) P W M 1m 1m 1m Determine the deflection at midspan
A load Pis supported by a structure consisting of rigid bar ABC, two identical solid bronze [E = 12200 ksi] rods, and a solid steel [E = 31000 ksi] rod, as shown. The bronze rods (1) each have a diameter of 0.72 in. and they are symmetrically positioned relative to the center rod (2) and the applied load P. Steel rod (2) has a diameter of 0.54 in. Assune Ly=59 in and L2=89 in. If all bars are unstressed before the load Pis applied, determine the normal stresses in bronze rods (1) and steel rod (2) after a load of P = 16 kips is applied. (2) (1) L2 (1) |L1 O B C Answers: i ksi. i ksi.
-2.4m- 8 mm 200 mq 8 mm 250 mm 8mm The steel beam has the cross-sectional area shown. The beam is loaded as shown with the intensity of the distributed loading w=70 kN/m. Determine the absolute maximum bending stress in the beam in MPa.
The stepped shaft ACB shown in Figure bellow is fixed at both ends and loaded by a torque TO at point C. Segment AC having solid circular cross section and segment CB having hollow circular cross section. If the shafts material is steel with shear modulus G = 11 x 10°psi, and the torque is To = 8,000 lb-in. Calculate: (a) The maximum and the minimum shear stress in segment CB. (b) The maximum and the minimum shear strain in segment CB. (c) The angle of rotation Ø, at the cross section where the torque To is applied. 0.75 in. 3.0 in. A 4000011Ww То 6.0 15.0 in. 2.4 3.0 0.75 in. in. in.
The stepped shaft ACB shown in Figure bellow is fixed at both ends and loaded by a torque TO at point C. Segment AC having solid eircular cross section and segment CB having hollow eircular cross section. If the shafts material is steel with shear mođulus G = 11 x 10 psi, and the torque is T, = 8,000 lb-in. Calculate: (a) The maximum and the minimum shear stress in segment CB. (b) The maximum and the minimum shear strain in segment CB. (c) The angle of rotation 0, at the cross section where the torque To is applied. 0.75 in. 3.0 in. -15.0 im. OF F 2.4 3.0 0.75 in. in.
PROBLEM 6 The rigid bar DC below is horizontal under no load, and bars A and B are unstressed. When the load P is applied, the strain in bar B is found to be 0.0015. Determine (a) the factor of safety with respect to failure by slip for bar A. (b) The load P (c) The vertical displacement (deflection) of point C. E B A C 100 mm 100 mm 50 P. 200 mm 375m m
2.4 m- 2.4 m- 8 mm 2.4 m 200 mm HHHH 8 mm 250 mm 8 mm The steel beam has the cross-sectional area shown. The beam is loaded as shown with the intensity of the distributed loading w=70 kN/m. Determine the absolute maximum bending stress in the beam in MPa.
Example The beam ABC is loaded via a 500 N.m couple and a 600 N force as shown. ... The beam is connected to the rest of the system by a pin joint at B and a roller support at ... Determine the magnitude of the reaction forces on the beam at the supports.
The torques shown are exerted on pulleys A and B. Knowing that both shafts are solid, determine the maximum shearing stress in (a) in shaft AB, (b) in shaft BC. T₁ = 300 N-m 30 mm TB =400 Nm 46 mm 20 A B C
For the beam shown, the magnitude of the distributed load is wo = 10.6 kN/m and the beam lengths are a = 6.3 m and b = 18.9 m. (a) derive equations for the shear force V and the bending moment M for any location in the beam. Place the origin at point A. (b) use the derived functions to plot the shear-force and bending-moment diagrams for the beam. Use your diagrams to determine the maximum shear force and the maximum bending moment. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number. Wo В a
Q3: Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that d₁ = 30 mm and d₂ = 50 mm, find the average normal stress at the mid- section of (a) rod AB, (b) rod BC. 125 KN B 80 KN 123 AN 1 1.2 m 0.9 m
A symmetrical beam of length 300 mm is loaded witha force of 414 N downwards (positive z) and has the following equation for the vertical displacement: w (2) = , ( - ) _F (zA El, 48 L²z² + The value of E is 200,000 Nmm2 and the values of ly is 20 x 10° mm4 The maximum value of z for the beam cross section is 20 mm What is the maximum tensile stress in the beam at the point when x = 90 mm?