English
Hindi

Question

Download Solution PDF

A body is loaded elastically so that strain in y-direction (ey) = 0 and σz = 0. Take σx and σy as finite. What is the value of strain in z-direction (ez) in terms of stress in x-direction (σx), Young's Modulus (E), and Poisson's ratio (v)?

This question was previously asked in
UPSC ESE (Prelims) Civil Engineering 19 Feb 2023 Official Paper
Download PDF Attempt in App
View all UPSC IES Papers >
  1. ez = σxv(1 + 2v)/E
  2. ez = σxv(1 - 4v)/E
  3. ez = σx(1 + v)/E
  4. ez = -σxv(1 + v)/E

Answer (Detailed Solution Below)

Option 4 : ez = -σxv(1 + v)/E
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

Explanation:

Concept:

Calculation:

As we know,

Strain in y-direction 

where σx, σy and σz are normal stresses in x, y and z-directions.

So, 

Now, strain in z-direction, 

using above relation         

 or ez = -σxv(1 + v)/E { where μ = v}

Download Solution PDF
Latest UPSC IES Updates

Last updated on Jul 2, 2025

-> ESE Mains 2025 exam date has been released. As per the schedule, UPSC IES Mains exam 2025 will be conducted on August 10. 

-> UPSC ESE result 2025 has been released. Candidates can download the ESE prelims result PDF from here.

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

‹‹ Previous Ques
Next Ques ››
Exams Tests Super Practice

More Simple Stress and Strain Questions

Q1.A steel bar (E = 200E = 200, α = 12 × 10 − 6/°C) expands by 0.3 mm due to  a temperature increase. If the original length of the bar was 15 cm, what was the temperature rise?
Q2.Determine the minimum thickness of the rectangular axial bar shown against yielding. Given Factor of Safety (FOS) = 2 and Yield stress = 310 MPa.
Q3.A prismatic bar of length 'L' and cross-sectional area 'A' is subjected to an axial tensile load 'P'. What is the maximum stress induced in the bar?
Q4.A mild steel rod of 14 mm diameter and 154 mm length elongates 0.025 mm under an axial pull of 10 kN. What is the Young's modulus of the material?
Q5.What will be the tensile force required to cause an elongation of 0.045 mm in a steel rod of 1000 mm length and 12 mm diameter, (where E = 2 × 106 kg/cm2)?
Q6.In generalized three - dimensional state of stress, the number of independent stress components is
Q7.Which of the following is correct representation of Poisson's ratio (μ)?
Q8.The ratio of tensile stress to the corresponding strain is a constant and this ratio is known as ____.
Q9._____ an be defined as time dependent increase in strain of a solid body under constant or controlled stress. 
Q10.Mention the sequence of points that mild steel material undergoes failure by referring to the stress strain diagram.
Suggested Test Series
View All >
UPSC ESE (IES) Civil Mock Test Series
116 Total Tests with 1 Free Tests
Start Free Test
UPSC ESE (IES) Electrical Mock Test Series
68 Total Tests with   0 Free Tests
Start Free Test

More Strength of Materials Questions

Q1.What will be the nature of longitudinal stress in a thin closed cylinder containing hydrostatic fluid pressure?
Q2.A steel bar (E = 200E = 200, α = 12 × 10 − 6/°C) expands by 0.3 mm due to  a temperature increase. If the original length of the bar was 15 cm, what was the temperature rise?
Q3.In the Charpy impact test, the specimen is typically:
Q4.Which of the following represents the polar modulus of the hollow shaft? [ If Do = External diameter and Di = Internal diameter ]
Q5.A simply supported beam with a span length of 5 m carries a moment of 20 N-m (counterclockwise direction) at the middle of the beam. What will the value of reactions be at both the ends of the beam?
Q6.What will be the shape of the bending moment diagram for a cantilever beam carrying a uniformly distributed load throughout its length?
Q7.If a component has a Factor of Safety (FoS) of 1.0, what does it indicate?
Q8.If elastic strength increases 3 times, then Proof Resilience:
Q9.If the external diameter of a hollow shaft is three times greater than its internal diameter, what is the ratio of its torque-carrying capacity compared to that of a solid shaft of identical material and the same outer diameter?
Q10.For a thin planar ring of radius ‘r’ mm and thickness ‘t’ mm, its radius of gyration about the polar axis in mm is:
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti all teen patti all games teen patti apk download teen patti game paisa wala