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

Define the pre-tensioned concrete construction We understand that in the pre-tensioned concrete construction, stretched tendons are provided in the concrete moulds at the time

Determine the term - Final Tension The tension in tendons after losses of prestress have taken place is called as final tension. Final tension is taken to be corresponding  to

Question What is key mechanism of defence by hot dip galvanizing ? Answer Hot dip galvanizing protects steel or iron from corrosion by- (i) It figures a metallic z

Maximum thermal stress in circular tapering section is

Figure, working,principle of prismatic compass

Compute the stresses at top and bottom fibres in a simply supported pre-stressed concrete beam with a rectangular cross section, 200 mm wide and 400 mm deep at sections A-A, B-B an

for calculating the bending moment in which the loading and the length of continuous beam is taken from the user

Pressure at Any Point on the Surface of a Horizontal Plane  Fluid pressure is the same at any point on the horizontal plane because: 1.  The fluid specific weight is the sam

Maintenance of Terminal Building: All accessories such as lighting, water, sanitation, telephone and public address system should be maintained in a good condition. Disposal