Problem

Formula Method-Statically Indeterminate Beams(a) Determine the reactions and draw the comp...

Formula Method-Statically Indeterminate Beams

(a) Determine the reactions and draw the complete shearing force and bending moment diagrams. Report the maximum shearing force and the maximum bending moment and indicate where they occur.
(b) Where deflection formulas are available, also compute the maximum deflection of the beam expressed in the form,
where EI is the beam stiffness, the product of the modulus of elasticity for the material of the beam and the moment of inertia of the cross section of the beam. The term Cd will then be the result of the computation of all other variables in the deflection equation for the particular beam support type, span length, and loading pattern.
(c) Complete the design of the beam specifying a suitable material, and the shape and size for the cross section. The standard for design must include the specification that bending stresses and shearing stresses are safe for the given material. Unless otherwise specified by the assignment, consider all loads to be static.
(d) Complete the design of the beam to limit the maximum deflection to some specified value as given by the assignment. In the absence of a specified limit, use L/360 as the maximum allowable deflection where L is the span between supports or the overall length of the beam. The design must specify a suitable material, and the shape and size for the cross section. This assignment may be linked to part b where the deflection was calculated in terms of the beam stiffness, EI. Then, for example, you may specify the material and its value for E, compute the limiting deflection, and solve for the required moment of inertia, I. The shape and size of the cross section can then be determined. Note that any design must also be shown to be safe with regard to bending stresses and shearing stresses as in part c.