A machine of mass m=500 kg is mounted on a simply supported steel beam of length l=2 m having a rectangular cross section (depth: 0.1 m, and Young's modules E=2.06x1011 N/m2. Find the natural frequency of transverse vibration. width:1.2 m)

A paper mill processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50-m outside diameter (OD) x 0.22-m inside diameter (ID) x 3.23-m long and is on a simple supported, hollow, steel shaft with Sut = 400 MPa. Find the shaft ID needed to obtain a dynamic safety factor of 2 for a 10-yr life if the shaft OD is 22 cm and the roll turns at 50 rpm with 1.2 hp absorbed. gear d key T cast iron roller a bearings are self-aligning so act as simple supports

The beam shown in Figure Q.2 consists of a W610 x 140 structural steel wide-flange shape [E =200 GPa; /= 1120 × 106 mm²]. If w = 62 kN/m and P= 123 kN, determine: AV, V 1.5 m B W 3.5 m P 2.5 m D X

Figure attached.

Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 = 19kN. a W1 L/2 W2 Multiple Choice Answers Multiple Choice Answer: Axial force at point A (kN, tension positive): a. 3.31 b. 31.97 c. 37.33 d. 31 Multiple Choice Answer: Displacement at point B (mm, positive to right): a. 0.0061 b. 0.0395 c. 0.0193 d. 0.0261 Axial force at point A (kN, tension positive): Displacement at point B (mm, positive to right): L/2 P1 P2 (type in your multiple choice answer, e.g. a, b, c or d) (type in your multiple choice answer, e.g. a, b, c or d)