Question

Figure 2 shows a schematic diagram for a telescopic crane. It consists of 2 telescopic beams, where Beam 1, length 2 m, and Beam 2, length L. Beam 2 can slide in Beam 1. The beam is supported with a hydraulic ram such that it can be lifted up and down. The dimensions of beam cross sections are as shown Figure 3. At a particular instant, it is lifting a box that weighs W kg as shown. P1, P2, P3 and P4 are pin joints. a Evaluate the maximum tensile stresses in Beam 1 and Beam 2 Evaluate the maximum transverse shear stress in Beam b 1 2 m L m P1 P4 P3 BEAM 2 1.6 m BEAM HYDRAULIC RAM W Figure 2 telescopic crane assembly and loading 120mm 104mm 200mm 184mm 8 mm 5 mm (i) Beam 1 (ii) Beam 2 Figure 3 Dimensions of beam cross sections

L = 2.4 m

W = 1000 Kg

Common Data: [Young’s modulus, E=210 GN/m²]  [Poisson’s ratio, ν=0.33] [Yield stress σ₀ = 210 MN/m² ]

Answer 1

Given A cron consists of two beam f. and 2 2m Lm o 1.6m/ B Bu ฟ By tano = 16 0 - 390 L=2.4m W = 10ooky from force balance young modulus, E= 210 hPa Tieldstres, o = 210 mpa AnBn Bcom 12omn Ay+ By = 9810 MA=0 Byx2 = 98104 (2+2.4) By = 21.582KN AY -11772 KN 200 Ana Bic 27 KN B4 tano 18mm tensile stres, A 27x103 Ba 7 = (26X120) – (104x184) of = 5.55 mea bending stress, of o mxyman ob 11772x100x 2coo go.smpa 120x2w² 104x1843 12 maximum tensiu stress in beem a (Othman aftob Elman = 96mpa 1 now transverse shear stres, in bema ofman Tmon=1.122 Emon = linx 11772 = 27mpa 90 X 120 - 104X184