problems for practice

8/9/2019 Problems for Practice

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Q1) Design a minimum mass spring (shown in Fig.) to carry a given axial load(called tension-compression spring) without material failure and while satisfyingthe performance requirement: the spring must deflect by at least D (in.)

Solution


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Q2) Design a minimum cost cylindrical tank closed at both ends to contain a fixedvolume of fluid V. The cost is found to depend directly on the area of sheet metalused.


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Q3) The step-cone pulley shown in Fig. is to be designed for transmitting a powerof at least 0.75 hp. The speed of the input shaft is 350 rpm and the output speedrequirements are 750, 450, 250, and 150 rpm for a fixed center distance of abetween the input and output shafts. The tension on the tight side of the belt is tobe kept more than twice that on the slack side. The thickness of the belt is t and the

coefficient of friction between the belt and the pulleys is . The stress induced in

the belt due to tension on the tight side is s. Formulate the problem of finding thewidth and diameters of the steps for minimum weight.

SolutionDetermine the objective in terms of weight of the step cone pulley system.Determine the constraints so as to have the belt equally tight on each pair ofopposite steps; the total length of the belt must be kept constant for all the outputspeeds.)


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Q4)Design a can closed at one end using the smallest area of sheet metal for aspecified interior volume of 600m3. The can is a right circular cylinder withinterior height h and radius r. The ratio of height to diameter must not be less than1.0 and not greater than 1.5. The height cannot be more than 20 cm. Formulate thedesign optimization problem.

Q5)Design a shipping container closed at both ends with dimensions b b h to

minimize the ratio: (round-trip cost of shipping the container only)/(one-way costof shipping the contents only). Use the following data:Mass of the container/surface area: 80kg/m2Maximum b: 10mMaximum h: 18mOne-way shipping cost,full or empty: $18/kg gross mass

Mass of the contents: 150kg/m3Formulate the design optimization problem

Q6)Design a uniform column of tubular section, with hinge joints at both ends,(Fig.) to carry a compressive load P = 2500 kgf for minimum cost. The column ismade up of a material that has a yield stress (y ) of 500 kgf/cm2, modulus ofelasticity (E) of 0.85 106 kgf/cm2, and weight density () of 0.0025 kgf/cm3. Thelength of the column is 250 cm. The stress induced in the column should be lessthan the buckling stress as well as the yield stress. The mean diameter of the

column is restricted to lie between 2 and 14 cm, and columns with thicknessesoutside the range 0.2 to 0.8 cm are not available in the market. The cost of thecolumn includes material and construction costs and can be taken as 5 W + 2d,where W is the weight in kilograms force and d is the mean diameter of the columnin centimeters.


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Example Figure 2 shows two frictionless rigid bodies (carts) A and B connectedby three linear elastic springs having spring constants k1, k2, and k3. The springsare at their natural positions when the applied force P is zero. Find thedisplacements x1and x2 under the force P by using the principle of minimumpotential energy.


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