Question

1- a ) sketch the state of stress on a square element of a material on the surface of a shaft with a circular crosssection subject to both torsional load and a tensile load. b) if we were using a cantilever beam what is unique about its neutral axis, how would it change with a cricular crosssection?

Answer 1

7:44 PM O 0.7KB/s, fall 21 Smunese Doudos P.Hoimes Cumont Opnios in Stress Transformation Colluda Often times, like in the case the pressure vessels that we studied Xin linng Detends his Pt.DS in the previcus lesson, the stress in one direction is really small Cclationa Eo Jang for auccessfaly ceterdng his Po rasntded compared with the other two When this is the case, it is convenient to neglect the small stress, and instead of evaluating the stress Paper: Jucking ot reometicalv.contined acting on a cubic element within the material we can examine the stress acting on a plane. Euckling ot geomericaly contined chelis Lucla Sin Montzlwo, Paul Costa, Mameo Pozaulis.. Tru Tyz +Try Tay TyE 3D Stress State Plane Stress These two states of stress, the 3D stress and plane stress, are often discussed in a matrix, or tensor, form. As we reduce the dimensionality of the tensor from 3D 2D, we get rid of all the terms that con tain a componentin the z direction, such that T- 0 0 0 Now that we've reduced our state of stress to two dimensions, we can learn how to transform the coordinates along which these stress components act into any coordinate frame we are interested in. Why wou ld we want do that? Well, take a look the image below. Wood > P Wood Glue Two pieces of wood, cut at an angle, and alued together. The wood is being pulled apart by tensile force P. How do we know the glued joint can sustain the resultant stress that this force produces? calculate the normal and shear stresses perpendicular transform We need and parallel to the joint Therefore e need to rotate ASSOciated with the angle of the alued icint Then we can evaluate the stresses along these new directions, x' and y AD Once we've rotated the coordinate system, we need transform the forces acting in the old coordinate frame to this new coordinate frame. That means, we must draw a detailed free body diagram. If we take the a differential element near the origin of the new each surface coordinate system, we can get the forces acting from the stress times the differential area. Tx'yAA AA