Engineering Answers

At a particular point in a structural member a two dimensional stress system exists where sigma x=60N/mm^2 sigma y=-40N/mm^2 and shear stress (xy) =50N/mm^2 if young's modulus =200000N/mm^2 and poisson's ratio =0.3 calculate the direct strain in the x and y directions and the shear strain at the point.

Listed below is a combination of stresses acting at a point and referred to axes x and y in an elastic material. Using Mohr’s circle of stress determine the principal stresses at the point and their directions for each combination. 

i) sigma x=-60 N/mm^2, sigma y=-36N/mm^2, shear stress (xy) =5N/mm^2

ii) sigma x=30 N/mm^2, sigma y=-50N/mm^2, shear stress (xy) =30N/mm^2

In crank and slotted lever quick return mechanism, the crank length is (100 +X )mm and the distance between the fixed center is (225+X)mm. The length of the slotted lever is (525+X)mm. Determine the ration of time of cutting stroke to time of return stroke. Also calculate the length of the stroke . Note where X is two digit number made from the last two digit of the registration number of the students For example if the reg. no. of the student is 11912081 then X=81 and crank length is 80+81=161mm Draw the neat and clean diagram with proper scale. Rough drawings will not be considered. 

The following consecutive readings were taken with a level and a 4-metre leveling staff on a continuously sloping ground at common intervals of 30 m:

0.855 (on A), 1.55 m, 2,335, 3.825, 0.455, 1.380, 2.055, 2.855, 3.455, 0.585, 1.015, 1.850, 2.755, 3.845 (on B).

The RL of A was 380.500. Make entries in a level book and apply the usual checks. Determine the gradient of AB.

A 30 m steel tape was standardised at a temperature of 20^o C and under a pull 5 kg. The tape was used in catenary to fix a distance of 28 m between two points at 40^o C and under a pull of 5 kg. Given that the cross-sectional area of the tape = 0.02 cm², total weight 470 g. Young’s modulus of steel = 2.1 X 10⁶ kg/cm, and coefficient of linear expansion = 11 x10^-6per ^oC, (a) find the correct distance between the points, and (b) find the value of pull for which the measured distance would be equal to the correct distance.

 The velocity components in a two dimensional flow are :

U = 8x^2 y - 8/3 y^3 And

V = -8xy^3 + 8/3 x^3.

Show that these velocity components represents a possible case of an irrotational flow.

For the velocity components given as : u = ay sin xy, v = ax sin xy. Obtain an expression for the velocity potential function.

The stream function for a two-dimensional flow is given by ψ = 8xy, calculate the velocity at the point p(4, 5). Find the velocity potential function ϕ.

If for a two-dimensional potential flow, the velocity potential is given by ϕ = 4x(3y - 4), determine the velocity at the point (2, 3) . Determine also the value of stream function ψ at the poins (2, 3).

The advertising alternatives for a company include television, radio, and newspaper advertisements. The costs and estimates for audience coverage are given in the table below:

TV newspaper radio

Cost per advertisement $2000 $600 $300

Audience/advertisemet $100,000 $40,000$18,000

The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?

(a) Formulate the problem above in mathematical model.

(b) Formulate the problem in standard form.

(c) Solve this business problem using the Simplex method.