Mechanical Engineering Answers

QUESTION 2 [14 Marks]

In a metal workshop a technician is tasked with making calculations on metal strength

properties. The technician is given two rectangular plates, one of steel and the other of brass

each 40 mm wide and 10 mm deep and these are placed together to form a beam 40 mm wide

and 20 mm deep, on two supports 1 m apart, the brass plate being on top of the steel plate. You

are required to calculate the maximum load which can be applied at the centre of the beam

given that the plates are either

(a) Separate and bend independently,

[6]

(b) Firmly secured throughout their length.

[8]

Given: The maximum allowable stress in steel= 112.5 N/mm2

and in brass = 75 N/mm2

.

Take Es = 2 X 105 N/mm2

and Eb = 8 X 104 N/mm2.

Compute the drying power Ea and the relative evaporation Er of an area covered with grass of Z. = 2 cm, and that of an adjacent area covered with trees of Z, = 70cm. Given that wind velocity U = 2.5 m/sec, Tair = 8°C, relative humidity = 0.3, Pair = 1.3 kg/m”, pw = 1000 kg/m”, Patm = 1013mb, Z = 2m, and net radiation Q = 90 W/m². Why the Ed of trees is higher than that of grass?

Complex poles and zeros. Sketch the root locus with respect to K for the equation 1 + KL(s) = 0 and the listed choices for L(s). Be sure to give the asymptotes and the arrival and departure angles at any complex zero or pole. After completing each hand sketch, verify your results using Matlab. Turn in your hand sketches and the Matlab results on the same scales

A slightly compressible oil is flowing in a volumetric, homogeneous reservoir. The oil has a viscosity of 2 cp, compressibility of 5 x 10-5psi -1 and formation volume factor of 1 RB/STB. The reservoir is represented by a three-gridblock system as shown: T The dimensions and the properties of all gridblocks are Ax=200 ft, Ay=100 ft, Az=20 ft, kx= 100 mD, and p=0.20. The initial reservoir pressure is 3,000 psia. The well in gridblock 3 is produced so that the well block pressure is maintained at 1,500 psia for all time >0. All the boundaries are closed. Find the pressure of gridblocks 1 and 2 at t=10 days with the implicit finite difference formulation and the time step At=10 days.

A column with one end pinned and another end fixed is made of carbon steel AISI 1020. The column is hollow round bar with internal radius of 20.0 mm, thickness of 3.0 mm and length of 2000.0 mm. Determine a) whether the columns will buckle inelasticity or elastically. (4 marks) b) the buckling stress if the column is subjected with 80N of axial force (8 marks) c) the critical buckling load for the column. (8 marks)

A 3.0 m long spreader, solid cross section with both ends pinned connection to wire rope carry a load of 10000kg. The material is AISI 1060 carbon steel. With factor of safety, 12 determine the following: a) Minimum dimensions of a square, solid cross section is permitted without having failure? (10 marks) b) Minimum dimensions of a square, hollow cross section with thickness of 5.0 mm without having failure? 

An Autonomous Landmine Sweeper is required to search and detect 8 landmines each of area 30 cm² placed in a circular surface area as shown in picture below. The circular test area is 165 cm diameter. While the Vehicle dimensions are 16 cm width and 22 cm length

A certain ideal gas has a constant R = 38.9 ft-lf f/lb m-R with k = 1.4. a) If 3 lb m of this gas undergoes a reversible nonflow constant volume process from 120 psia,740 oF to 140 oF find P2, ∆U, ∆H, Q, Work. b) If the process in “a” had been steady flow find work and ∆S.

In the spring system as shown in the figure below, each spring constant is ki=k2=1000 N/mm, k3=500 N/mm, k4=200 N/mm, and the applied load is F2=500 N, F300 N. (1) Find the stiffness equation of the spring system (KU=F). (2) Find the displacement of node 2 and node 3

The armor of a tank can be simulated by a slab of thickness L= 152mm (6in) that is insulated on the right hand side as shown in the Figure A below. The slab is infinite in the y-direction. The left hand side is exposed to enemy fire, that is, an explosion at the surface of the slab. The explosion can be simulated by a surface temperature that varies as shown in Figure B. For the time t>2b the left hand side can be considered as insulated. You are asked to find a) the temperature distribution in the slab, that is T(x,t) for the small time, that is t<2b. b) the temperature in the slab, T(x,t) for large time that is t>>2b c) Determine the length L of the slab such that the temperature does not exceed 150 F after 100 seconds Use a) carbon steel and b) Ni-Cr alloyed steel Tmax= 1500 F; b=1sec; The initial temperature of the slab is 80F a) kst= 43 W/m.K (high k) ρ=7801 kg/m3 cp=473 J/kg.K b) kNi-Cr= 19 W/m.K (low k) ρ=7865 kg/m3 cp=460 J/kg.K L Figure 1 B,Tmax (b,0) 0 T t (2b,0