Question

Task Four: A gantry crane must take a maximum load of 1000kg, a below in Figure 2, A eteel wire with a 4:1 pulley system is used to support the load. Steel wire can be purchased in 2.5mm, 3mm, 4.5mm, 6.25mm, 8mm and 12.7mm diameters. Using the stress - strain curve below (Figure 3), determine which diameter steel should be used. Use a safety factor of 3. If the length of the wire is 2m, how much does the wire stretch? (Elastic modulus 180 GPA) 3m Figure 2. Schematic of a gantry crane with a max load of 1000 kg. de%-425 0.1 0.15 Figure 3. Stress vs strain plot for Steel wire. The gantry crane above has a span of 3m. The top beam is to be made of a rod of structural steel with the properties below. What is the diameter of the rod required to ensure the safety of the load? Use a safety factor of 2 Table 2 es of structural steel Pro Value 220MPa 400MPa Using the dimensions of the beam determined above, what is the maximum deflection of the top beam of the gantw

Answer 1

FBD OF GANTRY CRANE Let diameter of rod �d� mm Given Length = 3m = 3000 mm Sigma_y = 220 MPa Sigma_TS = tau = 400 MPa E = 200 GPa = 200 times 10^3 MPa Factor of safety = FOS = 2 man^m load = 1000 kg = 1000 times 9.81 N = 9810 N Now, Sigma F_y = 0 implies A_y + B_y � 1000 times 9.81 = 0 implies A_y + B_y = 9810 N also Sigma M_A = 0 implies A_y times 3 � (1000 times 9.81) times 1.5 = 0 implies A_y = 4905 N Therefore B_y = 9810 � A_y implies B_y = 4905 N The diameter of rod will be decided by the man stress (Bending or shear) acting on the beam. Which will be ruled by maximum moment and maximum shear. Finding dia from, Maximum Bending Moment Side :- B.M_max = A_y (1.5) = 4905 times 1.5 = 7357.5 N-m = 7357500 N-mm \r\n