Question

For the beam in Figure 1, which is made of steel (E = 200 GPa) with a solid rectangular cross section 80 mm wide and 100 mm deep: • derive an algebraic expression for the deflection as a function of x = the distance from the left end, • hence also calculate o the slope at the left support, and o the deflection 2 m from the left support. 20 kn.m ८ & 12 kN/m र ८ 5m Figure 1 र A Write answers in the space provided below and submit this page, along with a cover page and all workings attached. Make sure you specify units where appropriate. V(x) = dv(0)/dx = V(2) =

Answer 1

12 kolm gokntom 4 -5m- loomm Bomm Calculate expression for deflection () slope at x=0 E = 2x105 N/mm² RATRB = 1245 RAY 5 -1845X2.5 -20 = 0 [RA - 34 KN TRB = 26 kN) Eldy – RAX -12%** – 20 60° elements - 347–67?_ 20130 EY = 34 x 3 - 674 - pox texte bounday conth & X-5Yo at X=0,Y=0

al x=o, yo at x = 5, 4-0 O= 34(5)2 -C(5)*_10(4)2 +0,45 12 0= 708.33 - 312.5 - 250 +0,45 = 145.83 +C, ys 19 = -29.167 EIY = 343 -674-1972 -29,167% 12 E = 2x105 N/mm2 #= 80x1003 = 6.664105 mm 4 T2 El = 2x105x6.667X106 n-mm2 EL – 1333.33 kn-m2 expression for deflection Y= 34x² - 6x 1px? _ 29.167* 1333.33 x = distance from y= defereetiona left at & support in (m) in (m)

Eldy - 1700² - 2x3 20x - 29.167 O at x=0 Eldy = -29.167 Codes - -.167 - 29.167 1333.33 X=0 = .021875 radian (11) deflection at x=2m. ElY = 343 -624-123X? _2951673 Putx= 2 Ely = 34x23 – 6424 - RX2 – 29.16742 12 El4 = 45.33 - 8 - 24 – 58.334 Y = 45,004 x 1000 1333.33 Y = 33.753 mm finally-

16) = (34x3 - GRY - 642-19,1616)/1333,33 dy () = .021875 radian V2) = 33.753 mm ona