Question

Beam deflection using singularity functions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - An I-Beam (W 16 x 100) is loaded as shown. Given: E = 206 · GPa I = 6.21 · 108 mm4 = 6.21 · 10-4m4 RB = 579 KN Rp = 639 KN RE= -138 kN The following constants of integration are given: • C1 (Slope) = -1880 kN m2 • C2 (Displacement) = 3820 kN m3 90 kN/m 5 m 5 m 5 m X=0

For the I-Beam, assess the magnitude of the displacement at location C?

0 mm

29.9 mm

44.9 mm

49.1 mm

76.4 mm

For the I-Beam, assess the displacement  at X = 7.3 m? (3 SIG FIGS, incl. sign)

Answer 1

swer:. gokiilm a de 3m 2m 1 sm Rg=579 KN Roger RE=-138 = 639 kal E: 206 bpa - 2067109 Pa I= 6.2 1x 10-4 me G--1880 KN :- = -1880 X/03 N-m2 G= 3820 KN-m3 = 3820x10 3 Ma mp3 13 Using inoclefieel clowble integaatiem iedhod:- gokallm B gokilm EId2y = Mx Daca Mar (0) + Role-2) () + R$(x-12) () + goxº (Lung ) + 90(x-1252 (- 2 Mac = 579(x-2) + 639(x-12) 64522-45(2-1272 cxh+6398 => Erdly = 579 (x-2 -12)/-45(x-1212 dx2

El die = 879(x+23+ G|- 15*8|4 68968-1974 -45(-1979 celety slepe I-45(x-12) 12 EIY = $79 (x-2)3 + cxtGI- 15x414 639 (x-12, 21 ūT -- deflection At c: X = 7.3 m Ct4 = 579x100 (7-3-2) 2 (-1880x103) 77.3 + 3820*103 - 15*7-34x103+0+0 EIYC = - 6186709.875 - - 0.04836 Ic=-6188709.875 - 2068 109 x 6.21810-4 Yo 5-0.04836 s Negative sign indicates Y deflection at a will be downward Ich 48.36mm Yo 5 49.1mm Answers