Prof.Kodali Srinivas

When a component is subject to increasing loads it eventually fails. It is comparatively easy to determine the point of failure of a component subject to a single tensile force. The strength data on the material identifies this strength. However when the material is subject to a number of loads in different directions some of which are tensile/compressive  and some of which are shear, then the determination of the point of failure is more complicated. Metals can be broadly separated into 'Ductile' metals and 'Brittle' metals. Examples of ductile metals include mild steel, copper etc . Cast iron is a typical brittle metal.Ductile metals under high stress levels initially deform plastically at a definite yield point or progressively yield. In the latter case a artificial value of yielding past the elastic limit is selected in lieu of the yield point e.g 2%proof stress.  At failure a ductile metal will have experienced a significant degree of elongatio

Mohr's circle is a graphical representation of a general state of stress at a point. It is a graphical method used for evaluation of principal stresses, maximum shear stress for a given normal and tangential stresses on any given plane. This method invented by German civil Engineer  Otto Mohr in 1882. It is extremely useful because it enables you to visualize the relationships between the normal and shear stresses acting on various inclined planes at a point in a stressed body. Mohr's Circle for Plane Stress  To establish Mohr's Circle, we first recall the stress transformation equations for plane stress at a given location, sq  = ( s x+ s y) /2 + ( s x- s y) /2cos2 q  + t xysin2 q  - - (1) tq  = ( s x- s y)/2sin2 q  -  t xycos2 q  -- (2) Adding the two  equations (1) and (2) after squaring  the equations and  Using a basic trigonometric relation  we have,                         ( s q - s ave ) 2   + t 2 q = R 2   W here            

Principal Plane and Principal Stress It is the Plane in which only normal stress is acting without Shear Stresses is called principal plane. The normal stresses which are acting on Principal Plane are called as Principal Stress. Sign Conventions: 1.Tensile normal stress is considered as positive and compressive normal stress is considered as negative. 2. Shear stress acting on a face is considered positive if it rotate the element in clockwise direction and negative if in anticlockwise direction. Stresses on Oblique Plane The normal stresses ( s x  and   s y ) and the shear stress ( t xy ) are acting vary smoothly on a body, the normal and tangential stresses or shear stress acting on a Oblique plane making a rotation of an angle  q    to the vertical face are given by, Normal stress on inclined plane   s q = ( s x + s y )/2 + {( s x - s y )/2} cos 2q +  t xy  sin 2q                                                                       -- (1) She

Question Bank: S.M.2, Unit -1 Short Answer questions 1. Define the term obliquity and explain about Normal and tangential stresses on an inclined plane.  2. Define the terms principal planes and principal stresses   3. Find the principal stresses and the principal planes at a point, if Normal stresses are acting in X and Y axis along with shear stress.  4. Explain graphical method for locating principal axes. 5. Define and explain maximum strain energy theory.  6. Discuss briefly the maximum principal stress theory 7 Discuss in brief various prominent theories of failure Short Answer questions - Mohr's circle of stresses 1.If the element is subjected only normal stresses equal and opposite in nature the Mhor's circle is shown in figure.  In this case pure shear stresses are exit in a plane of 45 degrees to normal stress plane and equal to normal stress. 2.If the element is subjected only normal stresses unequal and same in nature the Mo