Determine the normal and shear stress elements, Civil Engineering

Determine the normal and shear stress elements:

The state of stress at a point is given through the stress components σx = 70 MPa, σy = 10 MPa, and τxy = - 40 MPa. Using Mohr's circle find (i) Principal stresses, and (ii) Principal planes. Also, determine the normal and shear stress elements on planes making 25o, 40o and 60o associatively along with the x plane.

838_Determine the normal and shear stress elements.png

Figure

Solution

(a)        Choose (σ, - τ) coordinate system to a suitable scale.

(b)        Mark the points X (70, - 40) and Y (10, + 40).

(c)        Draw a circle with XY as diameter. This circle cuts σ axis at A and B.

(d)        Measure the coordinates of A and B to obtain principal stresses

σ1  = 90 MPa,  σ2  = - 10 MPa

(The radius of the Mohr's circle gives τmax = 50 MPa)

(e)        Measure ∠ XOA ; Here, ∠ XOA = - 52.8o .

∴          Aspect angle Φ1 of major principal plane is - 26.4o.

(f)        Measure ∠ XOB ; Here, ∠ XOB = + 127.2o

∴          Aspect angle Φ2 of major principal plane is + 63.6o.

(g)        Draw radial lines OR, OS and OT making angles 50o, 80o and 120o with OX.

(h)        Coordinates of R give the normal and shear stress components on the plane which makes 25o with the x plane. Here,

σn  = 28 MPa, τnt  = - 48.5 MPa

(i)         Coordinates of S given the normal and shear stress components on the plane which aspect angle 40o. Here,

σn  = 5.7 MPa, τnt  = - 36.8 MPa

(j)         Coordinates of T give the normal and shear stress components on the plane with aspect angle 60o. Here,

σn  = - 9.5 MPa, τnt  = - 6.5 MPa

Posted Date: 1/30/2013 6:24:48 AM | Location : United States







Related Discussions:- Determine the normal and shear stress elements, Assignment Help, Ask Question on Determine the normal and shear stress elements, Get Answer, Expert's Help, Determine the normal and shear stress elements Discussions

Write discussion on Determine the normal and shear stress elements
Your posts are moderated
Related Questions
Q. What are rules for working of Dip lorries and their protection arrangements on a single line section explain with sketches? Ans.-Rules for working of Dip lorries - i. Sub

Q- What is the difference between painting, polishing and varnishing as for as woodwork is concerned? What are their advantages and disadvantage? Ans. - Painting - P

Q. Explain about Overhauling of Level xing? Each level crossing except those laid with PSC sleepers must be opened out and the condition of sleepers and fittings, rails and fas

Describe the features of physical survey phase The Physical Survey (field and laboratory test) for the purpose of determination of physical and engineering properties of the ma

With a clear sketch indicate the system of protection of line for works of short duration where ‘ Stop dead restriction' need to be observed on a single line section on a BG track.

About Doors,windows&vendilators

Define Cast iron substructure - Inspection of bridge? Cast Iron also has the problem of corrosion due to atmosphere, which is similar to that of steel. However, in acidic or br

natural phenomenon affecting the designs of harbours

Ask questiPermanent Way:on #Minimum 100 words accepted#

design of timber in flexural members in terms of extreme fibre stress in bending, maximum horizontal shear stress, deflection and bearing stress perpendicular to the grain. the ful