Question

Consider a cantilever beam of rectangular cross section that is rigidly mounted to a wall on one side and then loaded by a force on the other side that is at a slight angle from the vertical. Due to the slight misalignment by an angle alpha the usual bending stress formulae will be inaccurate and formula for calculating the normal stress with components of the induced moments caused by the misaligned force must be considered. For the beam in question the breadth is B = 0.099574 meters, the height is H = 0.1858 meters and the length is L = 3.268186 meters. A cartesian coordinate system is used to model the geometry of the beam such that the cross section that is rigidly mounted to the wall lies in the yz-plane where the origin of the coordinate system is coincident with the centroid of the cross section where x = 0 meters and the cross section at the end of the beam is subjected to a force P = 2.962256E4 newtons where x = 3.268186 meters where P is applied in a downwards direction (i.e. in the negative y-direction) such that the angle in radians is alpha = 0.061225 radians where alpha is the acute angle between the vector of the force P and the negative y-axis. The geometry system is such that the top surface of the beam lies in the plane where y = H/2, the bottom surface of the beam lies in the plane where y = -H/2, the front surface of the beam lies in the plane where z = B/2, the back surface of the beam lies in the plane where z = -B/2, the end cross section that is rigidly mounted to the wall lies in the plane x = 0, and finally the cross section that is subjected to the inclined load lies in the plane x = L. For this problem calculate, taking in account the induced moments caused by the misalignment, the corresponding normal stress sigma

Answer 1

Answer:

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