The rod shown in the figure has two cross-sectional areas, where the area of the larger cross-section is 6 times larger than the smaller. The rod is subjected to three point loads, P₁, P2, and P3 at points B, C, and D, respectively. You may assume that the bar deforms in a linear-elastic manner. The cross section of the small rod is equal to A = 2 in² and the modulus of elasticity is equal to E = 20,000 ksi. a) Find the support reactions at A and E, if P₁ = 10 kips, P2 = 20 kips and P3 = 40 kips. b) Draw the axial force diagram. c) Identify how the position of point C changes due to the applied loadings. A 12 in B P₁ 11 in C P₂ 11 in D P3 12 in E

The rod shown in the figure has two cross-sectional areas, where the area of the larger cross-section is 6 times larger than the smaller. The rod is subjected to three point loads, P₁, P2, and P3 at points B, C, and D, respectively. You may assume that the bar deforms in a linear-elastic manner. The cross section of the small rod is equal to A = 2 in² and the modulus of elasticity is equal to E = 20,000 ksi. a) Find the support reactions at A and E, if P₁ = 10 kips, P2 = 20 kips and P3 = 40 kips. b) Draw the axial force diagram. c) Identify how the position of point C changes due to the applied loadings. A 12 in B P₁ 11 in C P₂ 11 in D P3 12 in E

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: A bar made of A-36 steel has the dimensions shown in Figure. If an axial force of P = 80 kN is…

Q: 1- The two uniform linearly elastic rods shown below are welded together at B, and the resulting…

Q: Q 3 A square steel bar 50 mm on a side and 1 m long is subject to an axial tensile force of 250 kN.…

Q: Question 2) The Russell fracture traction device and a mechanical model of the leg are shown in the…

A: L = 100 cmW = 250 NIt is asked to find the tension T1, T2

Q: Q3) The rigid bar ABCD is supported by bars (1) and (2). After load P is applied, the normal strain…

A: Given that, The strain in bar 1, ε1=20 μm/m, The deflection in bar 1 is, Strain in bar 1 is given…

Q: A member is formed by connecting two steel bars shown below. Assuming that the bars are prevented…

A: Given Data: The decrease in total length is, δH= -0.68 mm. The elastic modulus of steel is, E=206…

Q: investigate whether the safety requirement

Q: For the element shown in the figure, replace the distributed load with the equivalent nodal forces.…

A: To replace the distributed load with equivalent nodal forces, we need to calculate the forces at…

Q: A bar of a uniform cross-section is rigidly fixed at one end and loaded by an off-centre tensile…

A: GivenF=2.5 kNσallow=269 MPah=17 mmb=48 mm

Q: Q2: A 75 mm diameter compound bar is constructed by shrinking a circular brass bush onto the outside…

Q: Q2 / (A) The vertebra of the spinal column can support a maximum compressive stress of omax , before…

A: The load is not applied at the axis, it is applied with some eccentricity, and because of the…

Q: Three uniform cross-section rods, two of material A and one of material B, transmit the tensile…

Q: Consider the bar in Figure 2, which has cross-sectional area A = 1-10-3 m², modulus of elasticity…

Q: What, if any, are the stresses at point O? NOTE THAT WE ARE NOW ASKING ABOUT POINT O. Choose all…

A: When a bar is subjected to various loads then there are different types of stresses developed in the…

Q: When an axial load is applied to the ends of the bar shown in the figure, the total elongation of…

Q: Q1) Bar (1) of length 2.8 m and bar (2) of length 0.73 m are fixed at ends A and C. There is a A =…

Q: Four axial forces are applied to the 25mm thick structural steel bar with 40mm diameter pins as…

A: The given force member is as shown below,

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

The rod shown in the figure has two cross-sectional areas, where the area of the larger cross-section
is 6 times larger than the smaller. The rod is subjected to three point loads, P₁, P2, and P3 at points
B, C, and D, respectively. You may assume that the bar deforms in a linear-elastic manner. The
cross section of the small rod is equal to A = 2 in² and the modulus of elasticity is equal to E =
20,000 ksi.
a) Find the support reactions at A and E, if P₁
=
b) Draw the axial force diagram.
c) Identify how the position of point C changes due to the applied loadings.
A
12 in
B P₁
11 in
C
10 kips, P₂ = 20 kips and P3 = 40 kips.
P₂
11 in
D
P3
E
the axu
12 in

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Calculation of reaction force at end A and E

VIEW

Step 3: Calculation of deflection of C

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Bar (1) has a length of L1 = 2.4 m, and bar (2) has a length of L2 = 0.63 m. Initially, there is a gap of A = 3.8 mm between the rigid plate at Band bar (2). After application of the loads P to the rigid plate at B, the rigid plate moved to the right, stretching bar (1) and compressing bar (2). The normal strain in bar (1) was measured as 3159 um/m after the loads P were applied. Determine the normal strain produced in bar (2).
A light ridig member AB is pinned at A and is further supported by light elastic rods CD and GF, member AB supports a 5000lb load at B the elastic modulus for the two elastic rods CD and GF is given as E= 30x106 psi and the cross-sectional area for each of these rods is 1 in2. what are the forces in the two supporting elastic rods as a results of the loading?
A rectangular bar of length L has a slot in the central half of its length. The bar has width b, thickness t, and elastic modulus E. The slot has width b/3. The overall length of the bar is L = 520 mm, and the elastic modulus of the material is 74 GPa. If the average normal stress in the central portion of the bar is 190 MPa, calculate the overall elongation of the bar. Answer: 6 = b IN -1/2- b 6/3 mm
A heavy spool rests on the ground at point A and against the wall at point B. Find force F required to pull the cable off the spool in the direction shown, given:Mspool = 100 kg, rI = 200 mm, rO = 460 mm, μ = 0.2 for all surfaces.
Problem 3.1 A tie rod and a strut are used to support a force, P = 51 kN, as shown in the figure. The rod AB is made of a material with Young's modulus equal to 96 GPa and has a cross-sectional area of 450 mm². Strut BC is made of a material with Young's modulus equal to 180 GPa and a cross-sectional area of 1450 mm². The angle, a, is 52 degrees. Determine the horizontal and vertical displacement of point B. ВС 45° a P 1 m
The bar shown in diagram is subjected to a tensile load of 150 kN. If the stress in the middle portion is limited to 160 N/mm2, determine the diameter of the middle portion. Find also the length of the middle portion if the total elongation of the bar is to be 0.25 cm. Young's modulus is given as equal to 2.0 × 105 N/mm2. 150 KN ➜ 10 cm DIA 45 cm 10 cm DIA 150 KN
Let's consider a rod having a solid circular cross-section with diameter of 5 mm and it is made of a material having a Young's modulus E = 200 Gpa and a Poisson's ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 4.995 mm. determine the applied force F. Select one: O F = 5236 N O F = 6283 N %3D O F= 13090N O F = 10472 N O F= 15708N OF=4189 N 9:22 PM EN ? 4/15/2021
Consider the bar in Figure 2, which has cross-sectional area A = 1·10−3 m2, modulus of elasticityE = 1·1011 N/m2, and length 1 m. The bar is fixed to a wall on its left hand side. Along the left halfof the bar, x=[0 m, 0.5 m], there is a constant distributed force of l(x) = 10 kN/m. Along the righthalf of the bar, x=[0.5 m, 1 m], there is a constant distributed force of l(x) = 20 kN/m. a) Given the finite element mesh in Figure 3, consisting of two elements of equal size L = 0.5 m,sketch the associated basis functions of the mesh, and write the approximation of the displacementfunction u(x) as an expansion of these basis functions. Use u1, u2 and u3 to denote the expansioncoefficients for each node. b) The general form of the element stiffness matrix system, with nodes indexed by i and j, is givenas shown in the image of eqaution 2, where F0 and f(1) denote boundary forces at positions x = 0 and x = 1, respectively. Form the two basis functions for element 2, and evaluate the right…
In the figure below, a member is subjected to an axial force P. If the cross sectional area of the member is denoted as AB, then the maximum value of its shear stress occurs when: ∅ = 00 ∅ = 300 ∅ = 450 ∅ =900
Mechanics of materials I
A rectangular steel block is 3 inches long in the x direction, 2 inches long in the y direction, and 4 inches long in the z direction. The block is subjected to a triaxial loading of three uniformly distributed forces as follows: 48 kips tension in the x direction, 60 kips compression in the y direction, and 54 kips tension in the z direction. If the Poisson’ Ration is 0.30 and the modulus of elasticity is 29xksi, determine the deformations at each direction. Also, determine the single uniformly distributed load in the x direction that would produce the same deformation in the y direction as the original loading.
2.6 The truss ABC shown in the figure supports a horizontal load P₁ = 9 kN and a vertical load P₂ = 18 kN. Both bars have cross-sectional area A = 1,290 mm² and are made of steel with E= 210 GPa. a) Determine the strain energy U₁ of the truss when the load P₁ acts alone (P₂ = 0). b) Determine the strain energy U₂ when the load P2 acts alone (P₁ = 0). c) Determine the strain energy U when both loads act simultaneously. 813 mm 1524 mm P₁ = 9 kN P₂ = 18 kN