Calculate the principal stresses for the state of stress, Civil Engineering

Calculate the principal stresses for the state of stress:

Calculate the principal stresses and principal planes for the state of stress shown in Figure.

2431_Calculate the principal stresses for the state of stress.png

Figure

Solution

Given σx = 60 N/mm2

σy = 20 N/mm2

τxy = - 26 N/mm2

On substituting in Eq. (6), we get

2303_Calculate the principal stresses for the state of stress1.png

∴          σ1 = 72.8 N/mm2 and σ2 = 7.2 N/mm2

Again substituting the values σx, σy and σxy in Eq. (2).

tan 2Φ = 2τxy/σx-σy = 2×(-26)/60-20 = -1.3

Since θ is general angle, the specific angles representing the principal planes are designated as Φ1 and Φ2.

∴          2Φ = - 52.43º, 127.57º

using    2Φ = - 52.43º

σn = (60 + 20/2) + (60-20/2) cos (-52.43o)- 26 sin (- 52.43º)

=72.8 N/mm2

Hence, we recognize that Φ1 = - 52.43º/2 defines the major principal plane and therefore, Φ2 = 127.57o/2 should define the minor principal plane.

Posted Date: 1/30/2013 6:13:19 AM | Location : United States







Related Discussions:- Calculate the principal stresses for the state of stress, Assignment Help, Ask Question on Calculate the principal stresses for the state of stress, Get Answer, Expert's Help, Calculate the principal stresses for the state of stress Discussions

Write discussion on Calculate the principal stresses for the state of stress
Your posts are moderated
Related Questions
Q. What is Stilling basins? Stilling basins are usually introduced to convert supercritical flow to subcritical flow before it reaches downstream. A typical stilling basin comp

Q. Axial flow pumps for large flows and low heads? It is well known that axial flow pumps are the most suitable for providing large flows and low heads. Reason behind this is c

Question What is problem in traditional marine piling system of steel tubular pile with concrete infill and what are key possible remedial measures? Answer In design

Define Divers in a team for Underwater inspection of Bridge? One team of divers should have minimum three members. This is a requirement of safe working. The idea is while a mi

three points problem

finding the mean ,mode and mediam

what is wmm what are all the uses of that wmm

what is grillege foundation and where are use

Binomial Distribution - exact probability: For the binomial distribution having n = 10, y = 0.4, find p (X ≤ 4) using equations and verify that equation gives a better approxi

Explain the Dynamic or Vibration Tests Tests of this type, also known as sonic integrity test, involve sub- jecting the element to a single impulsive blow or cyclic load, and