Principal Stresses Highlights Principal planes (i) Principal planes are at right angles to each other and are given by tan2θpp = 2 τ/( σx — σy) In this σx and σy are assumed to be tensile. Two values of tan 2θ will give two values of 2θpp. These will be 2θpp1 and 2θpp2 such that 2θpp2 = 2θpp1 +1800. Hence θpp2 = […]
Principal stresses-Assignment At a point in an elastic material under strain, the stresses on three mutually perpendicular planes are follows: A normal tensile stress of 60 N/mm2 and a shear stress of 40 N/mm2 on one plane, a normal compressive stress of 40 N/mm2 and a complementary shear stress of 40 N/mm2 on the other […]
mcqs: Principal stresses- 2 Mohr’ s circle is a graphical method to find (a) Bending stresses (b) Principal stresses (c) Torsional shear stresses (d) None (ANs: b) Mohr’s stress circle method is used to analyze a body under (a) Complex stresses (b) Tensile and compressive stresses (c) Axial and longitudinal stresses (d) None (Ans:a) When does […]
mcqs: Principal stresses-1 A principal plane is a plane of (a) Zero tensile stress (b) Zero compressive stress (c) Zero shear stress (d) None (Ans: c) A principal plane is a plane of (a) Only normal stress (b) Only shear stress (c) Only bending stress (d) None (Ans: a) There are in all (a) Two […]
Short Interview Question Answers- Principal stresses Q. What is angle of obliquity? A. Any plane is to be under complex stress if it has a normal and shear stress simultaneously. Then there will be a resultant stress. The angle between the resultant and normal stress is called the angle of obliquity and is represented […]
Mohr’s Stress circle GRAPHICAL METHOD: MOHR’S STRESS CIRCLE METHOD We know from the analytical method that σθ = (σx + σy)/2 + ((σx — σy)/2) (Cos2θ) + τ Sin2θ τθ = (( σx — σy)/2) (Sin2θ) — τ Cos2θ Square and add, we get the equation of a circle as given below. [σθ – (σx — σy)/2)]2 +τ2 = [(1/2) (σx — σy) […]
Ellipse of Strain ELLIPSE OF STRAIN It is the locus of the resultant strain on the infinite inclined planes within a body under principle strains. It is a graphical method to find the resultant strain and the angle of obliquity on a given inclined plane (with the plane of major principal strain). CONSTRUCTION Being […]
Ellipse of stress Introduction Ellipse of stress is used to find resultant stress and the angle of obliquity on any plane within a stressed body. In 2-D, it is called ellipse of stress . In 3 D it is called ellipsoid of stress. Actually all bodies are 3-D. All stress systems are also 3-D. But […]
PRINCIPAL STRESSES Number of forces are acting simultaneously almost on each body. Thus, it is complex loading condition. When these forces increase, a body fails by a simple principal stress or by maximum shear stress. COMPLEX STRESS SYSTEM When normal and shear stresses act simultaneously on an area (plane), it is called a complex […]
Principal Stresses-Analytical Method In this, it is required to determine principal planes, angle between principal planes, principal stresses, planes of maximum shear, angle between planes of maximum shear, maximum shear stress from the given complex stress system. There are two methods to determine all the above quantities. (i) Analytical Method (ii) Graphical Method or Mohr’s Stress Circle Method […]