Question

2. [24 p.] A 1.2 kg steel ball is dropped on a cantilever beam from a height of 2.1 m, see below The beam material is steel (E 200GPa) Calculate Maximum impact force (g = 9.81 m/s2) Maximum deflection of the beam - a. b. PL3 3EI 2lw Deflection Formula: ? ?.aess secTION Ocm lcvn

Answer 1

Since this is a case of Impact loading So In this we define a loading factor called Impact factor. If (Impact factor is given by) If = 1 + squareroot 1 + 2h/delta_Static delta_Static rightarrow deflection due to static force = static force time if & maximum deflection = static deflection times if Now, We will calculate delta_Static delta_static = Pc^3/3EI when p = mg = 102 times 9.81 times 1063/3 times 280 times 10^3 times 1/12 times 10^4 = 23.544 times 10^03 mm = 23.594 times 10^-16 m L = 10 cm = 100 mm I = 1/12 times h^4 = 1/12 times 10^4 mm^4 Therefire LF = 1 + squareroot 1 + 2 times 2.1/23.544 times 10^-6 = 423.3629 Therefore (a) Impact forace - F_state time LF = mg times LF = 4983.83 N (b) Max deflection = 9.9677 times 10^-3 m m 9.9677 mm