Question

Mechanics of Materials

Need step by step setup without numbers

Q2. (35%) Flexural Stress and Shear Stress Consider the simply supported beam below. The beam is constructed from steel that has an elastic modulus of XXX. Assume the centroid to be located XXX from the bottom of the shape, and the moment of inertia to be YYYY. a) Determine the beam reactions b) Determine the M- and V- diagram or function for the beam (you can use either method) c) At the section with maximum positive moment determine the maximum flexural stress in the cross-section. d) At the section with maximum negative moment determine the maximum flexural stress in the cross-section. e) At the section with maximum shear force determine the shear stress 1 inch below the centroid. Include a sketch that shows your dimensions used in calculating Q. f) To determine the maximum shear stress in a cross section, highlight in a new sketch the cross-section area included in the calculation of Q.

Answer 1

82 Assumptions elastie modulus X XXX Controid = XXX Momentof inrtia 4444 Simply su pportet beam Simply supporta) beam with U.D.L assum W=y * Reaition foras ZMA= 0 th. sam of momenFabout at th. point A -W, X4X4%2+RBX4=. M MR= 0 th. sum of moment about atthe point R - RA X4 + W, Xyx(4-%½) = 6 substitude W=4 nd solue O 8O RA= 8 We will RB = 8

shror force and brding mment diagram Uniformly distributedid-ay shar fore diagrom Bending arant diegrom M. Flera'ral strosus Wilth positive bending moment pritia. bonding mmn: Top fibns de in compresion Bottom fibres re in Lension My The fierural strees :0= M= Moment where We com calculate FS y: distonce betroces centraid to th. point. f inertia. at the cenfer point of the Mom ont Moximom flezuwal streses :- beom we com get maximum FS

At centre point of th. beom we com qet marimum flexurol stross Nigative bending momunt Top fibres in compression fomion BOHDN fibres.cole in Flexural stresses o= MY