Question

Considering the above system determine the following information 21 (15) 22 Derive the equation of deflection of the beam using the second order flexural equation EL = M(I), Utilize your previously derived solution to obtain the beam deflection dg at the (5) point B where I = 0; Utilize your previously derived solution to obtain the beam rotation Og at the (5) point B where I = 0, 23 Total Marks: [25] Hints for Question 2 (i) You can assume that the bending moment is M(x) = -m(L - x), (u) The beam rotation is calculated from the formula 0 = deste

Answer 1

a uniform yaxis farmiy distributed the m unit SA Cantileuer beam AB is acted upon by moment of intensity per along beam of the m OC MA B А L VA from point B Take a section 7-x at distance a X Moment about 1-7 MX - - mx А B Using x second order flexural equation EI day - ma 0 daca Integrating above ega. We get EI dy da ma2 t C, 2 2 Again Integrating, we get FIG + Ciz + C2-3 mi 6 is - Deflection of bean) given as, - MX3 taiat Cz x + (2] - yo [ mais 4 cs Scanned with CamScanner

2.2] Boundary condition : At 1-L rotation le 0 dy and deflection (y) da will be Zero x=L dy :o & goo di from en @ EI dy da - mx ² tci 2 at L = L 7 dy =o dx -mi? tci 2 Ci= ML? 2 at x=L7 yo gi ei l-me? + Cl +(2) - 0 C2 = ML3 • CIL 6 ML3 - ML3 2 6 C2 - ML3 3 CS Scanned with CamScanner

the values of constant cr & ce we get Substituting [ - ma g + ML2 x - ML3 2 3 1 EI deflection at B ciie 2-0) OB = (o to-mea - m ) EI OB - ML3 ЗЕІ negative sign indicates deflection downward direction 2-3] EI dy -mx² + ML? 2 2 da Rotation at pt B Cie OB) OB=0+ ml? 2EI 2 OB- ML? 2 EI cs Scanned with CamScanner