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
the jet transport B is flying north with a velocity vB = 600 km/h when a smaller aircraft A passes underneath the transport headed in the 60 degree direction shown. To passengers i


Q. Can you explain Permeable Spurs? A permeable spur may be constructed by driving two or more rows of bally piles with sufficient penetration below riverbed level to provide a

Define Circular Channels Flowing Partially Full Two sets of curved lines on the Circular Channel Ratios figure (discharge Q/Q full and velocity v/v full ).  1.  "n" variabl

Determine the stage of Cracking moment of pre-stress  At the stage of transfer of pre-stress in the pre-stressed beam element, only the pre-stressing force and the self weight

Define Sounding or Sensing Devices? Sounding devices are effective in checking scour in the streambed adjacent to a bridge. Although sounding/sensing devices can be used indepe

Earthquake force analysis method Dynamical method In contrast with the static loading, dynamical analysis method is discussed. In this method, structure reflections at any poin

how to solve ild and rolling load problem for shear force and bending moment with the diagram.

Compute the thermal stresses in steel: Consider the compound bar shown in below figure consisting of a steel bolt of diameter 18 mm, surrounded through a copper tube of outer

the nick name of FeS is fool''s gold-explain