Question

Determine the midspan deflection for the beam loaded as shown in Fig. P-677.

w N/m N 를 - - RI R₂ Figura P-677.

Answer 1

find reaction first يقين c A st Ź we 1/2 TR2 Ri Determine mid span deflechim. we know, equation of elastic curve Ifv = 0 Rith 2 = Rat R₂ = wl 4 EMA = 0 R, х -I wil x 1 x 1 to R2 wl 24 Rii - wl w of Gel-wl 24 24 Ri= 5 we 2. 3 2 Eld²Y E-M da² 24 where x is distance measured M = Bending stress Y = deflection E1 - jie tural sigidity

1/61 Wh = wt 4 using macaulay's wolory swl.a 24 - we (x-1) 1/2 wl 24 4 sol 24 we a Know El dy da? EI dy -5 wla 24 it wl (x-1) he da? 4 Integrate both side El dy twl -5 wl x² da 24 2 +(, at + C2 Integrate both side Ely = -5 48 At support deflection is so 2=0, y=0 zero. olt omit +/c, xo + C2 =) (₂=0

term Ale to macaulay's theorm, if any parantheses comes out should be omitted. in -ve, am it Now put a=l, y=0 t wel (8) -5 we. e3 +C. l 144 2V G.l= 5 144 wie 125 wl 5184 SS we3 {l is cancelled 5184 from both side we get 1 put , & lz in equo ELY wla3 144 wol 24 (x-1) +55 wex 5784 th for mid span deflection, put a = +55 x wi. A El mid EII mid 2 3 of 144 5184 us wil && wel 1152 of 55 wey 72 648 10368 + 13 wy" 5184 EI Ymid