Given is a truss structure: Where: • Working shear stress for the rivets is 70 MPa • Working bearing stress due to rivets is 140 Mpa • Thickness of the member is 5 mm • Thickness of the Gusset plate is 6 mm • Rivet diameter is 15 mm Determine the no. of rivets to fasten the member BD 50 kN 30 kN 5m 4 m 4 m c 4 m E 3m

NOTE: 1. The following are grounds for not considering your solution and final answers: a)Figures not properly labeled. b)Equations that are not consistent with the firgure. C)Equilibrium equations do not have sign conventions. d) unsequenced solution. e) answers without units 2. Computations accurate to the nearest tenths. Problem. Show that the following structures are statically determinate and determine the support reactions. b) B is pin connected, C is fixed, hinge supports A and D. 8 kN 8 kN 2 m -2 m 3 kN/m C 4 m D -3 m

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A differential element on the bracket is subjected to plane strain that has the following components: , strain at x = 250 x 10-6, strain at y = 300 x 10-6,  strain at x y= -500 x 10-6. Use the strain-transformation equations and determine the normal strain strain x' in the x' direction on an element oriented at an angle of 35°. Note, a positive angle is counter clockwise.

Write the number of elements, nodes required and degree of freedom to solve following truss using FEM (Use the best node/element numbering; Do not need to solve it!) Would ANSYS be able to solve the structure with given Boundary Conditions (BC)? If not, what should be done and why?

Why should an element subjected to maximum shear stress be oriented?

For fluid undergoing circular motion, the centripetal force is provided by a pressure difference. Consider a fluid element (density p) at radial distance r, which has thickness dr in the radial direction and surface area dA normal to the radial direction. The pressure difference gives rise to a force on the fluid element equal to (p(r + dr) – p(r))dA. (i) Equating the pressure difference to the centripetal force, find an expression for the radial pressure gradient in terms of p, r, and fluid velocity v. (ii) A fluid is undergoing body rotation in the r-0 plane (cylindrical polar co-ordinates). By considering the gravitational pressure head, show that the shape of a free surface z(r) is parabolic. (iii) Find and sketch a similar expression for the free surface of a fluid vortex produced by a rotating cylindrical spindle (i.e. a solid cylindrical rod) of radius Ro.

STRUCTURAL THEORY