# Principal stresses-Assignment

** 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/mm
^{2}and a shear stress of 40 N/mm^{2}on one plane, a normal compressive stress of 40 N/mm^{2}and a complementary shear stress of 40 N/mm^{2}on the other plane, and

(a) Principal stresses and principal planes

(b) The maximum shear stress and its plane

(c) The position of the plane on which there is no normal stress

ANS(^{+ }74 N/mm^{2}, –54 N/mm^{2}, 19^{0}, 109^{0}, 64 N/mm^{2}, -69^{0})

2. The stresses at a particular point in a piece of material act upon the three planes whose relative angular positions are given by a triangle ABC, in which B is a right angle and angle C is 30^{0}. The normal stresses on these planes are 70 N/mm^{2} tension on AB, 30 N/mm^{2} compression on BC and 40 N/mm^{2} tension on AC. Determine the magnitude and direction of the shearing stresses on the given planes and the magnitude of the greatest direct stress and the greatest shearing stress at the point.ANS [ –52 N/mm^{2}, + 69.3 N/mm^{2}, 92.1 N/mm^{2} & 721 N/mm^{2}].

3.Direct stress of 120 N/mm^{2} tension and 90 N/mm^{2 }compression are applied on a elastic material at a certain point on planes at right angles. The greater principal stress is limited to 150 N/mm^{2}. What shearing stress may be applied on the given planes and what will be maximum shearing stress at the point? [135 N/mm^{2}]

4. The principal stresses at a point in a member subjected to two dimensional stress are 120 N/mm^{2} and 50 N/mm^{2} both tensile. Find the plane on which the resultant stress has maximum obliquity and the magnitude of this obliquity. [ 57^{0 }9’, 24^{0}18’]

5. At a point in a stressed body, the normal stresses are 90 N/mm^{2} tension on a vertical plane and 30 N/mm^{2} compression on a horizontal plane. A negative (clockwise) shearing stress of 50 N/mm^{2} acts on the vertical plane at that point. Determine and show on a sketch the principal and maximum shearing stresses. Also calculate and show normal stress on the plane of maximum shear stress.