Question

PLEASE SHOW ALL WORKING. MAKE SURE ITS NEAT PLEASE. WILL GIVE GOOD RATINGS IF EVERYTHING MAKES SENSE AND IN GOOD SHAPE

02 A 3-point bend test is performed on a rectangular beam of steel as shown in figure Q2. Equation Q2.1 shows how the vertical displacement () varies with position along the beam (x). Equation Q2.2 indicates how the second moment of inertia depends on the breadth (b) and height (h) of the rectangular cross-section. Eq.2.1 bh 12 Eq.2.2 Using the data in Table Q2 below, calculate the value of I and its uncertainty (a) (61 Obtain an expression for E, the Young's modulus, by re-arranging Eq2.1 and using the data in Table Q2 estimate the value and uncertainty in E (b) [141 F= 1000 ± 10 6- (0.050 ± 0.001) h(0.005 :0.001) L-(0.500+0.001) Load on Beam Breadth of Beam Height of Beam Length of Beam Position along Beam Displacement of Beam (0.250+0.001) y= (7.2 ±0.1)×10" m TABLE Q2 FIGURE Q2

Answer 1

SOLUTION GIVEN DATA LOAD ON BEAM F= Hevaht Geam Lenath ofBeam position along Beam χニ(0.25010001)nn Displacement of Beam y-(3.210-1)xo" h- (0.OOS to.ool)กา กา uncertainty us notuing but ne rod of Rangth iom but de to manutaumina i- maj greater that 10m στ leas than 10 m , 10.2m and mnumum possioa (lo t2)m and He un antain Hera the n certain Sumpe duvivativ @cuv): uav tva-ב 12 6b= O.OS1-0.049 = 0.002m

pulting a nece sny 3x o.os х(o.oos), ooo2 + 0 oo53XO.002 Δェ 12 12 3 12 in momant o area 1 0 (a 2EI re amanging thaaove ea 2. 0.2s 12 3 ピリ9: C ογ both side to lot a il Caretue

(yL) 6(y1)2 12T) 2. 231 1241 2yI 2.

2 Now pultng 2 x 20 子, 2 x 16" x 5.2x10 2. 1-935 xO un cantaint taken as maSn △E = 8.616x10 12