FOUR THREE.

, ,

L-3ff -2/1PE Date: 06/04/2019BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-3/T-II B. Sc, Engineering Examinations 2017-2018

Sub: IPE 311 (Material Handling and Maintenance Management)

Full Marks: 210 Time: 3 HoursThe figures in the margin indicate full marks,

USE SEPARATE SCRIPTS FOR EACH SECTION

SECTION-AThere are FOUR questions in this section, Answer any THREE.

I. (a) Describe the technical factors that should be considered while selecting conveying

equipment with relevant examples, (12)(b) Name different types of intermediate supports generally used in conveyors, Write

down the required characteristics of an intermediate support, (5)(c) How can you increase the amount of pull (W0) in a conveyor belt without increasing

the tight-side tension using a snub pulley? (6)

(d) For a belt conveyor, having troughing idlers and conveying bulk material, derive the

equation for belt width, If the belt conveyor with troughing idler is horizontally

conveying sized bulk material (lump size, a' = 15 mm) having bulk weight, 'Y = 0,65

ton/m3, and dynamic angle of repose 13,5°, at a speed of 0,9 rn/sec and the required

capacity, Qris 5 tons/hr, find the minimum width of the conveyor belt, (7+5=12)

2, (a) Write down the advantages of apron conveyor. (5)(b) In a factory, unit loads (500 mm x 400 mm x 300 mm) are carried in an apron

conveyor followed by a roller conveyor horizontally in perpendicular directions a show i

figure 2(b), Each load weighs 10 kg and the spacing between two consecutive loads, a =

1000mm,

(i) In the apron conveyor, the conveying speed is 0,5 rn/sec, Flanged apron of width

750 mm is to be taken, A = 110 and ro' = 0.1. If two bush-roller chains are used to,pull the apron, find the capacity, maximum tension in each of the chain and, required

motor power for this conveyor (transmission efficiency is 90%, K = 1,08, and k' =

0,04), (10+10=20)(ii) In the roller conveyor, the roller diameter is 100 mm and the journal diameter is

55mm. Rolling and sliding friction factors are 0,005 m and 0,15 respectively, Ifpitch

(distance between consecutive rollers) is selected to be 1/4 of the length of the load

conveyed, mass of each roller rotating part is 0,5 kg, and the load is conveyed at a

speed of 0,75 rn/sec, find the hourly capacity, required motor power and the number

ofloads simultaneously carried on the conveyor (transmission efficiency is 95%),

Contd, """"" P12

"

=2=IPE 311Contd. to Q. No. 2(b)

~~'-'t'-'"~

Apr.,," C<1IlIilO of"

'-

, . ~. __flg~2Jl1.L ~(c) Explain the advantages of roller conveyor with neat sketches. (10)

3. (a) A screw conveyor conveying crushed stones (y = 1.8 tons/m3) to a height of 9 m from

the ground is designed to carry a maximum of 1000 kg of axial load at a capacity of II

tons/hr. The length of conveying run is 35m. Loading efficiency is 20% and transmission

efficiency is 72%. Resistance to motion factor is 4.0 and the friction factor between the

material and trough surface is 0.63. Find-

(i) Maximum possible rpm.

(ii) Screw diameter.

(iii) Required motor power.

Table 3.1: Table for value of inclination factor C.

I ~ (degree) I~1

20

0.65

(15)

Table 3.2: Table for maximum and minimum rotating speeds of the screw for heavy

abrasive material

Screw diameter D, mm 400 500 600

n,rpm Minimum 9.5 9.5 7.5

Maximum 47.5 47.5 37.5

(a) Suppose, in a factory a bucket elevator is employed to elevate wet ashes. What type of

bucket, bucket arrangement, speed, method of charging and discharging should be used

for this purpose? Justify your answer with neat sketches.

(b) Define lump size for sized and unsized bulk materia!s.

Contd P/3

(15)

(5)

. ,

=3=

IPE 3114. (a) For a bucket elevator prove that, polar distance, 1= 8925 , where n is the rpm of the

n

driving pulley. Also show that, the method of discharging is dominated by centrifugal

force when the length of polar distance is less than the driving pulley radius. (10+8=18)(b) Define the four basic types of layouts with examples. Suggest preferable material

handling devices for these layouts. (8)(c) Explain the features and applications of different types of buckets used in bucket

r

elevators.

SECTION-BThere are FOUR questions in this section. Answer any THREE.

All notations have their usual meanings.

(9)

5. (a) "Maintenance" must be an integral part of the production strategy for the overall

success of an organization. - Do you agree? Explain why. (10)(b) What is the difference between serviceability and maintainability? Discuss factors

responsible for the importance of maintainability. (10)(c) Define three broad indices that can be used to evaluate overall performance of an

organization with respect to maintenance and briefly explain each of them. (15)

6. (a) What are the main objectives of preventive maintenance? Discuss at least five

important elements of PM. What are the benefits and drawbacks of performing PM? (15)

(b) If total downtime per unit of time and failure rate ofa system is defined by (20)

TDT(n)= 'A(n) +~Jl e

'A(n)=fe-n

Where f is the system failure rate at n = O.Show that optimal value of n can be expressed

by

If repair rate, mean of exponentially distributed inspection times and system failure rate

at n = 0 of the above system are 50/month, 0.005 month and I failure per month,I

respectively, calculate the optimum inspection frequency for this system ..

7. (a) Two independent and identical machines form a parallel system. Each machine's

times to failure are exponentially distributed with a mean time to failure of 150h. The

periodic PM is performed after every 75h. Determine the system mean time to failure

with and without performance of periodic PM.

Contd P/4

(8)

=4=

IPE 311Contd. to Q. 7

(b) What are the various measures associated with corrective maintenance? Discuss

strategies for reducing the system-level corrective maintenance time.

(c) An engineering system can fail in two mutually exclusive failure modes. Failure

modes I and II have constant failure rates of "I = 0.002 failures per hour and "2 = 0.005

failures per hour, respectively. The constant corrective maintenance rates from failure

modes I and II are Ilcl = 0.006 repairs per hour and flC2 = 0.009 repairs per hour,

respectively. Draw the system transition diagram and calculate the system steady state

availability.

8. (a) The current layout of a factory is shown in figure 8(a). As shown in the figure, the

layout consists of eight (08) separate uniform cubic spaces (10m x 10m) and the central

bay is 2 m wide. From-to chart for frequency of movement in a week is shown in Table

8(a).

Raw material LatheFoundry shop

warehouse Milling shop mach inc shop

I Entry Exit I

Assembly Grinding FinishedOflice goodsshop warehouse ..

~'~, ".,

Fig. 8(a)

The company is willing to reduce the material handling cost by improving the layout.

They have figured out that the foundry shop is undesirable to keep near to either of the

warehouses.

(i) Develop the activity relationship chart using the information provided.

(ii) Propose an improved layout for the factory. Use the center-to-center distance to

generate the From-to chart for distance. Also calculate the amount of material

handling saved from the improvement.

Contd PIS

(12)

(15)

(30)

, . ••

=5=

IPE 311Contd. to Q. 8(a)

Table 8 (a) : From-to chart for frequency of movement in a week.

Office Raw Foundry Lathe Milling Grinding Assembly Finished

materials shop machine shop shop goods

warehouse shop warehouse

Office - 20 3 4 3 2 20 14Raw 4 - 36 28 10 5 0 0

material

warehouse

Foundry 2 0 - 10 15 30 1 0shop

Lathe 3 0 20 - 30 10 15 10machine

shop

Milling 2 0 5 10 - 30 20 10shop

Grinding 10 0 0 5 8 - 40 30shop

Assembly 22 0 0 2 I 2 - 50Finished 28 0 0 0 0 1 15 -goods

warehouse

(b) How can you improve the tensile strength of rubberized textile belt? Explain with

figure. (5)

,L-3!T-2/IPE . ~ Date: 10/04/2019

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKAL-3!T-2 B. Sc. Engineering Examinations 2017-2018

Sub: IPE 315 (Operations Management)

Full Marks: 210 Time: 3 HoursThe figures in the margin indicate full marks.


SECTION-AThere are FOUR questions in this section. Answer any THREE.

I. (a) EOQ and EPQ are two different inventory models. EPQ has two phases namely

production phase and usage phase, whereas EOQ has only one phase - why? (6)(b) Briefly discuss the following three capacity options in Aggregate Planning: (12)

(i) Hire and Layoff workers(ii) Overtime/Slacktime(iii) Part time workers

Mention their benefits over the other options.

(c) Time study is calculation but work sampling is estimation - justify. (5)(d) For the following task table, calculate the minimum number of work station and

corresponding line efficiency for a desired output rate of90 units in 2 hr time: (12)

Task Predecessor Time (sec)A --- 65B --- 50C A 35D B 45E C,D 38F E 53G E 29H F,G 41I H 33J H 48

Show the assignment of tasks to the required minimum number of workstation.

2. (a) In the present manufacturing sector, productivity growth is preferred over productivity

-why? (5)(b) Briefly discuss the alternatives if the current capacity of a factory is fully utilized. (15)(c) For the following order table, select the best sequence of jobs to be processed based

on FCFS, SPT and EDD rules with logic for your selection: (15)

Job Processing time (day) Due Date (day)A 5 7B 3 6C 7 10D 9 IIE 6 9F 8 8

Contd P/2

=2=IrE 315

3. (a) What are the two primary applications of work sampling? Provide example for both. (8)

(b) Briefly explain the four building blocks of JIT system. (12).(c) Based on the following data, select the best machine to be purchased with following

two conditions:

(i) No loss allowed

(ii) Need to satisfy market demand

Machine Fixed cost (BOT) Capacity (Unit)

A 75,000 500

B 100,000 800

C 120,000 1000

Demand - 800 ....;1000 unit

Revenue - BOT 200/unit

Variable cost - BOT 70/unit

(15)

4. (a) Few of the assumptions for EOQ model are not applicable for EPQ model- why? (8)

(b) Calculate EOQ and corresponding total cost for the following data: (15)

Annual demandOrdering costHolding costCost per unit

= 1000 unit= $ 15/order= $ 4/unit/year= $ 20 for lot size I - 99

$ 19.75 for lot size 100 -199$ 19.60 for lot size 200 - 299$ 19.45 for lot size 300 - 399$ 19.30 for lot size 400 - up

For 250 working days per year, if daily production is 10 unit and lead time is 7 days,

calculate EPQ and ROP.

(c) For the following job table, find the best sequence of jobs to be processed based on

Johnson's rule. Also show the schedule for each job:

JobProcessing Time (hr)

Station I Station 2 Station 3

A 4 3 7

B 8 2 5

C 7 4 6

0 5 I 8

E 6 3 4

Contd P/3

(12)

,

0'

=3=IPE 315

SECTION -BThere are FOUR questions in this section. Answer any THREE.

5. (a) The manager of the Carpet city outlet needs to be able to forecast accurately thedemand for Soft Shag Carpet (its biggest seller). If the manager does not order enoughcarpet from the carpet mill, customers will buy their carpets from one of the Carpet city'smany competitors. The manager has collected the following demand for the past months ..

(15)

MonthDemand for Soft ShagCarpet (1000 Yd)

I 82 123 7

5 95 15

6 11

7 10

8 12

(i) Compute a 3 period weighted moving average forecast for month 4 to 9. Assign2.5 times more weight for the most recent data compare to the third recent data and1.5 times more weight for the second recent data compare to the third recent data.(ii) Compute MAD, MSE and RMSE for the period 4 to 8.(iii) Find the production plan for the month 9 considering MAD value.

(b) Define different types of Product Layout and Process Layout. Also discuss their

relative advantages and disadvantages. (12)(c) What are the different issues need to be considered before selecting facility location? (8)

6. (a) Brown and Brown Electronics manufacture a line of digital audiotape (OAT) players.While there are differences among the various products, there are a number of commonparts within each player. The bill of materials, showing the number of each item required,

lead times and the current inventory on hand for the parts and components, follows: (20)

.~------_.- -~'.--~._~c----

- '/ E(2)

Contd P/4

=4=IPE 315Contd .. Q. No. 6(a)

Data for B: Gross requirement is 200 units on 9th week, Lead time is 2 weeks, Lotfor lot

Data for C: Lead time is 1 weeks, Lot for lot

Data for E: Lead time. is 2 weeks, lot size 200 units

Data for F: Lead time is 1 weeks, scheduled receipt is 100, on hand inventory is50, lot for lot

Data for G: Lead time is 1 weeks, scheduled receipt is 100, on hand inventory is50, lot for lot

Data for H: Lead timeis 1weeks, scheduled receipt is 100, lot size is 200

Data for I: Lead time is I weeks, scheduled receipt is 60, on hand inventory is 65,lot for lot

Prepare a MRP schedule to satisfy demand.

(b) What are inputs ofMRP? Explain them with necessary examples. (15)

7. (a) For the machine-part matrix shown below, fonn cells using Direct Clustering Algorithm

(DCA) and, if conflicts exist, propose alternative approaches for resolving the conflicts. (20)

Part # Machine #1 2 3 4 5 6 7 8

I I I 12 I 1 13 I 1 I4 .1 I I5 I I I6 1 1 I7 1 I 18 I 1 19 I 1 I10 I 1 1

(b) In which cases do you need qualitative forecasting? Explain different types of

qualitative forecasting in detail.

(c) Discuss the effect of inaccurate forecasting in any business organization.

8. (a) For the following distance matrix, find the two most suitable locations to establish a

Bank based on lowest distance-weighted cost.

Location distance (km)

From A B C D Weight

A 0 15 18 19 0.9

B 15 0 23 22 1.2

C 18 23 0 13 0.81

D 19 22 13 0 1.11

Contd PIS

(8).

(7)

(10)

.'

•

•=5=

IPE 315Contd .. Q. NO.8

(b) Compute costs for three different production plans and select the best one with behind

your selection: (25)

- -January 'February March April May June Total I

Beginning Inventory 400Demand Forecast 1250 1700 1300 1650 1000 1200

Safety Stock (0.25 x Demand)Production RequirementWorking days per month 22 19 21 21 22 20

Ending Inventory

Average No of workers = 1." January February March April May June Total I\

Beginning Inventory 400,Working days per month 22 19 21 21 22 20

, ;lIvailable hrs per month (8hrs/day)

"Actual Production (5hrs/unit)Demand Forecast 1250 1700 1300 1650 1000 1200

Ending InventoryShortage cost ($5/unit) ,Safety StockUnit excessInventory cost ($1.5/unit)Straight time cost ($4/hr)

Total Cost I

Plan 1: C'onstant workforce - Varv inventorv and stockout

I/"

"

[,,

Minimum No of worker = '2•January February March April May June Total I

Production RequirementWorking days per month 22 19 21 21 22 20Production requirement per dayAvailable hrs per month (8hrs/day)Actual Production (5hrs/unit)Unit subcontractedSubcontracting cost ($20/unit)Straight time cost ($4/hr)Total Cost I

Plan 2: Constant low workforce - Subcontract

Plan 3: Constant workforce - Overtime No of workers = 38

---

January February March April May June Total IBeginning Inventory 400Working days per month 22 19 21 21 22 20Available hrs per month (8hrs/day)Actual Production (Shrs/unit)Demand Forecast 1250 1700 1300 1650 1000 1200Ending InventoryUnits available before overtimeUnits needed overtimeOvertime cost ($6/hr)Safety stock ,Unit ExcessInventory cost ($1.S/unit)Straighttirrie cost ($4/hr)Total Cost I

L-3ff-2/IPE Date: 31/03/2019BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-3/T-2 B. Sc. Engineering Examinations 2017-2018

Sub: IPE 319 (Quality Management)




1. (a) What is "Shewhart Cycle" in TQM? What are the four stages which one must go

through to get from 'problem-faced' to 'problem solved'? (15)

(b) Describe, in tabular form, the differences in process improvement (using TQM)

versus process innovation (using BPR). (20)

2. (a) It is argued that IS09000 is not an alternative to TQM, rather complementary. What

are the eight TQM principles behind IS09000 QMS to justify this?

(b) "By using sound manufacturing and process engineering practices, defects could be

removed from processes without the use of many statistical tools". Who said this? What

is the relevant theory behind this statement?

3. (a) Prepare a hypothetical "Exemplary FMEA Form". Give a brief analysis.

(b) There are some distinguishing characteristics ofTQM. Explain those in brief.

4. (a) What are the main evaluation criteria of MBNQA? (Note: sub-criteria are not

necessary, but points of the main criteria are required).

(b) What is Kaizen? How did Imai define it? Explain.

SECTION -8There are FOUR questions in this section. Answer any THREE.

5. (a) What is sampling error? Describe the most serious sampling error.

A pharmaceutical company is producing tablets. The mean weight of the tablets needs to

be 15 grams. From the past records, it has been found that the standard deviation of

weight of the tablets is 0.2 gram. As part of statistical quality control, samples of size 10

are taken and the mean weight was obtained as 15.5 grams. The level of confidence is

0.95. Test if the process is producing tablets as per target mean weights Also measure

type II error and the probability of detecting the shift of process mean.

(c) Write short note on interaction effects and their graphical presentation under Design

of Experiment (Full Factorial).

Contd P/2

(15)

(20)

(15)

(20)

(15)

(20)

(5)

(20)

(10)

',~ -"

. ".:::- "

=2=

IPE 319

6. (a) Which chart is preferable between X -R and X -S chart? Why? Explain with

example.

(b) Measurement of the flow rate of liquid is commonly a critical parameter in many

processes. Some applications, however, require the ability to conduct accurate flow

measurements to such an extent that they influence product quality. A new process was

studied in order to measure the flow rate. A sample of one unit is sufficient to ensure the

quality of the liquid The flow rate of 10 batches are listed below.

Batch Number Flow rate

I 49.6

2 47.6

3 49.9

4 51.3

5 47.8

6 51.2

7 52.6

8 52.4

9 53.6

10 52.1

(i) Suggest appropriate chart to solve the problem with explanation.

(ii) Develop the control limits and evaluate whether the process is in statistical control

(c) Describe five main aspects oflean manufacturing.

7. (a) What kind of charts are used to detect small changes in parameters?

(b) For an EWMA chart, fill the following table with I,= 0.25 upto day 3.

X=10.97,R=3.7 SampleSizen=5

Day (t) or, XI (gm) Range (R) Gt EWMA

sample m Control limits

LCL VCL

I 11.7 4.1

2 9.3 3.8

3 11.2 3.3

Contd P/3

(5)

(20)

(10)

(3)

(15)

=3=IPE 319Contd ... Q. NO.7

(c) A company and its customers agreed to follow a double sampling plan, with the

following paranleters,

Lot size N = 2000,

First sample size nl = 30, CI= 2

Second sample size n2= 80, C2= 4.

Population fraction nonconforming = 0.08Find the total probability of acceptance in the combined first and second sample.

(17)

8. (a) Describe the bath tub curve with appropriate diagram (10)

(b) Describe certification schemes on six sigma. (10)

(c) According to Taguchi's loss function, tolerances should be designed appropriately,

which requires a trade-off between two issues. Write down those issues. How many

defects per million opportunities are outside of the area created by the mean plus 3cr

standard deviation? (15)

•

,

.-'. ,

Table A. StlPdard Normal UistributiOn Values (AreaS under the normal curve).

0.4750

z 0 1.96

I 0.00 0.01 0.02 0.03 0.04 O.OS 0.06 0.07 0.08 0109z

00 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.OJ19 0.0359

01 0.0398 0.0438 0.047& 0.0511 0.0551 0.0596 0.06:16 0.0675 0.0714 0.0753

01 0.07'13 oom 0.0871 0.0910 0.0948 0.0987 0.1026 0:1064 0.1103 0.11.1OJ 0.1179 01217 0.12)5 0.1293 o.ml 0.1:168' 0.1406 0.1443 0.1480 0.1S170.' 0155' 0159' 0.1628 0.1664 0.1700 0.1736 o.m 0.1&08 0.1'''4 0.1179

'-'~',~'' 0.191S 0:950 0.19&5 0.2019 0.20S' 0.2088 0.2123 0.21S7 0.2190 0.2224I 0.2257 1')".QI O.2~:' 0.lll7 0.2389 0.2422 0204 0.2486 02517 0.2549

07 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 02813 0.n520.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3021 OJ051 0.3078 0.3106 OJm09 0.3'59 O.31X<, 0.3212 0.3218 0.3264 0.3289 .0.llIS 0.3)40 0.3165 0.3389

1.0 0.341) 0.3418 0.3461 0.148S 0.3S0& OJSII OJSS4 01577 0.359'1 0.3621:.1 0.36'3 0.3665 0.3686 (1.1708 OJ72'l 0.1749. 0.3770 0.3790 OJ810 0.3&3011 , 0.)849 03869 0,;888 0.3907 O.)925 0.)94' 0.3962 OJ9SO 0.';991 0.401SIJ O.40ll 0.4049 0.4066 0.4082 0.4099 0.41IS 0.4lll 0.4147 0.4162 0.4177

" 0.4'92 0.4207 0,4222 0."236 0.4251 0.4265 0.4279 0-4292 0.4306 04319

J.l 0.'))2 O.0434S 0.4357 0.4370 0.4382 0-4194 0.4406 0.4418 04429 . 0.44411.6 I 0.4412 0.4463 04474 0.4484 0.4495 O.• 5OS 0.4SIS 0.4525 . 0.'535 0.41451.7 u.oIIH~ 0.'564 0.457) 0.4582 o.•m 04599 0.4608 0.4616 0.4625 0-46Jl

'-8 04641 04649 0.4616 0.4664 0.•671 0.4678 0 .• 686 0.469) Q.4699 0.47061.9 I O.41Jj 0.4719 0.4726 0.4732 0.4138 0.4744 0.4750 0.4756 0.4761 0.4767

10 04772 0.4778 0.4183 0.4788 0.4793 .0.4798 0.4&03 0.'80& 0.4812 0.481711 0.4821 0.4816 0.4BlO 0.•1l4 0.•838 0.4842 0.4846 0 .• 850 o.•&s. 0.48il11 0.4861 0.•864 0.4868 0.4871 0.'875 04878 0.4881 0 .• 884 0.4817 0.48102.3 o'~"89J 0.'8% 0.'898 0.4901 0.•904 04906 0.4909 0.4911 04913 0.•9162.' .~4918 0.4910 0.4922 0.•915 0.4927 04929 0.49JI 0.932 0.49)4 0.4916

1 S ~0~)8 0"9'0 04941 0.494) 04945 04946 0.49.8 049'9 0.•9SI 0491216 04953 . O.c9H 04956 0.4957 04959 0.4960 0.4961 0.4961 0.4963 0.4%42 ; 0.4965 0'966 04967 0.4968 0.4969 o 497t' 0.49)1 04972 0.49';') 0.497428 0.4974 0.49i5 0."976 04977 0.4977 0,4978 0.<979 0.•• 79 049&0 0.98129 0498; . 0'982 0.4982 0.498) 0.4984 0.•984 0.4985 0498S 0'9" 0."86

) 0 , ~4987 ~ 4981 0.4987 0.4988 0.•988 0.4989 04989 04989 0.4990 0.4990._--- ---~ . -- ---~-

Table B.Factors used in 30 Quality Control Charts.

X ch4rts Sclwls Rchans

Sample Factors for CU'ltroI Pactors Factors~mils lor ccDU>1 F•••••• lor cOl1llOllimilS lor •••••••1 Factors for conttollimitssizcn Ii•• line

A A, A, Co B, B. B. S. d., d, D, 0, 0, D.2 2.121 1.880 2.659 0.7979 0 3.267 0 2.606 1.128 0.U3 0 3.686 0 3.2673 1.732 1.023 1.954 0.8862 0 2.568 0 2.276 1.693 0.888 0 4.358 0 2.5144 1.500 0.129 1.628 0.9213 0 2.266 0 2.088 2.059 0.880 0 4.698 0 2.2825 1.342 0.577 1.427 0.9400 0 2.089 0 1.964 2.326 0.864 0 4.918 0 2.1146 1.2.2S 0.483 1.281 0.9515 0.030 1.970 0.029 1.874 2.534 0.848 0 5.078 0 2.0047 1.134 0.419 1.182 0.9594 0.118 1.882 0.113 1.806 2.704 0.833 0.204 5.204 0.076 1.9248 1.061 0.373 1.099 0.9650 O.ISS 1.815 0.179 1.151 2.847 0.820 0.388 5.306 0.136 1.8649 1.000 0.337 1.032 0.9693 0.239 1.761 0.232 1.707 2.970 0.808 0.547 5.393 0.184 1.81610 0.90'9 0.308 0.975 0.9727 0.284 1.116 0.276 1.669 3.078 0.797 0.681 5.469 0.223 1.1771\ 0.905 0.285 0.921 0.9754 0.321 '1.679 0.313 1.631 3.173 0.781 0.811 5.535 0.256 1.74412 0.866 0.266 0.886 0.9776 0.354 1.646 0.346 1.610 3.258 0.778 0.922 5.594 0.283 1.71713 0.832 0.249 0.8S0 0.9794 0.382 1.618 0.374 1.585 3.336 0.770 1.025 5.647 0.307 1.69314 0.802 0.235 0.817 0.9810 0.406 1.594 0.399 1.563 3.407 0.763 1-1\8 5.696 0.328 1.672IS 0.775 0.223 0.789 0.9823 0.428 1.512 0.421 1.544 3.472 0.156 1.203 H41 0.347 1.65316 0.750 0.212 0.763 0.9835 0.448 1.552 0.440 1.516 3.532 0.750 1.282 5.782 0.363 .1.63717 0.128 0.203 0.739 0.9845 0.466 1-534 0.458 1.511 3.588 0.744 1.356 5.820 0.378 1.62218 0.107 0.194 0.718 0.9854 0.482 1.518 0.475 1.496 3.640 0.739 IA24 5.856 0.391 1.60819 0.688 0.181 0.698 0.9862 0.497 1.503 0.490 1.483 3.689 0.734 IA81 5.891 0.403 1.59720 0.671 0.180 0.680 0.9869 0.510 1.490 0.504 1.470 3.735 0.729 1.549 5.921 MI5 1.58521 0.655 0.173 0.663 0.9876 0.523 1.477 0"16 10459 3.778 0,724 1.605 5.951 0.425 ISIS22 0.640 0.167 0.647 0.9882 0.534 1.466 0.528 1.448 3.819 0.720 1.659 5.979 0.434 1.56623 0.626 0.162 0.633 0.9881 0.545 1.4S5 o.s39 1.438 U5a 0.716 1.710 6.006 0.443 1.557]A 0.612 0.1S7 0.619 0.9892 0.555 1.445 0.549 1.429 3.895 0.712 1.759 6.031 0.451 1.S4ll25 0.1100 0.153 0.606 0.9896 0.565 1.435 0.559 1.420 3.931 0.708 1.806 6.056 0.4~9 1.S41

.'L-3rr-2/IPE Date: 25/03/2019

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKAL-3rr-2 B. Sc. Engineering Examinations 2017-2018

Sub: IPE 329 (Numerical Analysis)




1. (a) For the free-falling parachutist with linear drag, assume a first jumper is 70 kg and has

a drag coefficient of 12 kg/so If a second jumper has a drag coefficient of 15 kg/s and a

mass of 75 kg, how long will it take him to reach the same velocity the first jumper

reached in lOs?

(b) The "divide and average" method, an old-time method for approximating the square

root of any positive number a can be formulated as

(10)

(12)

xx+a/x

2Make a well-structuredjlowchart and then write pseudocode to implement this algorithm.

(c) Because a decrease in step size can lead to subtractive cancellation or to an increase in

computations, the truncation errors are decreased as the round-off errors are increased.

How can you circumvent this problem?

(d) Briefly discuss the consequences of normalization in the floating-point representation

of numbers.

2. (a) The derivative of j(x) = 1/~ - 3x2 ) is given by

6x

(1-3x2 f

(8)

(5)

(10)

Do you expect to have difficulties evaluating this function at x = 0.577? Try it using 3-

and 4-digit arithmetic with chopping.

(b) Discuss a procedure for approximating the error in f(x) given the derivative of a

function and an estimate of the error in the independent variable. Use appropriate

sketches. (10)

(c) Prove that for a centered difference approximation of the first derivative, the

truncation error is of the order of h2 (10)

(d) Distinguish betweenjormulation error and data uncertainty. (5)

Contd P/2

=2=

IrE 329

3. (a) Determine the total flops as a function of the number of equations n for the

(i) decomposition, (ii) forward-substitution, and (iii) back-substitution phases of the LU

decomposition version of Gauss elimination.

(b) With the help of sketches, describe singular and ill-conditioned systems.

(c) Discuss the role of pivoting and scaling in solving system of linear equations.

4. (a) Derive three simultaneous equations for the four unknown constants for second-order

Runge-Kutta methods and prove that there is a family of second-order methods rather

than a single version.(b) Prove that the local truncation error for the Euler's method is proportional to the

square of the step size and the first derivative of the differential equation.

(c) Use the (i) Euler and (ii) Heul1 (without iteration) methods to solve.

d2~-t+y=Odt2

where yeO) = 2 and y'(O)=O. solve from t = 0 to 4 using h = 0.5. Compare the methods by

plotting the solutions.


All the symbols have their usual meanings unless specified otherwise.

(25)

(5)

(5)

(12)

(8)

(15)

5. (a) The function defined by /(x) = sin 1tX has zeros at every integer.

Show that when -1 < XI <0 and 2 <Xu <3, the bisection method converges to (15)(i) 0, ifx{ + Xu <2(ii) 2, ifxl + Xu > 2(iii) I, ifx{ + Xu = 2

(b) An object falling vertically through the air is subjected to viscous resistance as well asto the force of gravity. Assume that an object with mass m is dropped from a height So

and that the height of the object after t second is

s(t) = So _ mg t + m2g (1- e -kt / m )

k k2

Where g = 32.17 ft/s2 and k represents the coefficient of air resistance in lb-s/ft. Suppose

So= 300 ft, m = 0.25Ib, and k= O.llb-s/ft. (6+14)(i) Given Xo = 5 and E:s< 0.015%, wr.ite a MATLAB code based onjixed point method

to determine the time needed for the object to hit the ground.(ii) Given Xo = 5 and E:s < 0.015%, apply fixed point method to determine the time

needed for the object to hit the ground

6. (a) Derive Newton-Raphson iterative formulas for a system of three non-linear equations

and then generalize those formulas for a system of N number of non-linear equations. (20)Contd P/3

=3=

IPE 329

Contd ... O. No.6

(b) In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical

challenge of John of Palermo in the presence of Emperor Frederick II: Find a root of the

equation x3 + 2x2 + lOx= 20. He first showed that the equation had no rational roots and

no Euclidean irrational root - that is, no root in any of the forms

a :tJb,~:tJb,~a:t.Jb ' or ~~:tJb,where a and b are rational numbers. He then

approximated the only real root, probably using an algebraic technique of Gmar

Khayyam involving the intersection of a circle and a parabola. His answer was given in

the base-60 number system as

1+22Uo)+7uor +42US +33uor+4uoY +40UorUse secant method to approximate the same real root of the nonlinear equation as

approximated by Fibonacci. Use 1.4 and 1.6 as initial guesses. Perform three iterations

and calculate approximate percent relative error for each iteration. Compare your result

obtained after three iterations of the secant method with that of the result shown in the

base-60 number system. Comment on the accuracy of Fibonacci's approximation.

7. (a) Suppose that /(x), /(x j, and /(x) are easily computable.(i) Derive in algorithm like Newton-Raphson's method that uses three terms in the

Taylor series. The algorithm should take as input an approximation to the root and

produce as output a better approximation to the root.

(ii) Show that the method is cubically convergent.(b) In many engineering problems, a random variable cannot have negative values due to

the physical aspects of the problem. In this situation, modeling the variable as lognormal(i.e., considering the natural logarithm of the variable X) is more approximate,

automatically eliminating the possibility of negative values. The probability density

function of a lognormal variable is given by

I [_Htn~~AX r}fx(x)- ..n;, e , O:o;x< ex:

211 ~xxwhere J", and ~x are the two parameters of the lognormal distribution. These parameters

for a lognormal random variable, let X, can be calculated from the mean (fl.,) and the

standard deviation (CTx) of X using the following formulas:

I 2A,x=lnllx--~x

2

Contd P/4

(15)

(6+9)

. ".•

=4=

IPE 329

The probability that X is between a and b can be calculated as

b

P(a:5X:5b)= Ifx(x)dx"a

The mean compressive strength of a batch of concrete beam is found to have a lognormal

distribution with a mean value of 5,000 psi and a standard deviation of 500 psi. The

minimum required strength is 4,000 psi. Calculate the probability that the mean

compressive strength of a randomly selected batch of concrete beam is satisfactory.

While evaluating the integral for calculating the required probability, use the following:

(i) Composite trapezoidal rule, with n = 8;

(ii) Multiple application of Simpson's 1/3 rule, with n = 8;

(iii) Multiple application of Simpson's 3/8 rule, with n = 6.

Comment on the accuracy' of the results obtained in (i), (ii), and (iii).

[Hint: It might be more convenient and computationally efficient to calculate the

probability of the mean compressive strength of a randomly selected batch of concrete

beam being unsatisfactory and then subtract the result from I.]

8. (a) Consider the polynomial f(x) = x4 - 3x3 + x2 + X + I, part of whose graph is shown in

Figure for Q 8(a).

Approximate the largest real root using Muller's Method by performing the first two

iterations. ~"~---------~---------- ---------- - (15)

I0.5

-.1

-0.5

Figure for Q. tl(a)~------------(b) Use the nodes Xo = 2, XI = 2.75, and Xl = 4 to find the second Lagrange interpolating

polynomial for j(x) = IIx (8)(c) The Newton forward-difference formula is used to approximate j (0, 3) given the

following data.

X

j(x)0.0

15

0.2

210.430

0.6

51

Suppose it is discovered that j(O.4) was understated by 10 and j(0.6) was overstated by

5. By what amount should the approximation to j(0.3) be changed? (12)

••

L-3/T-2/1PE Date: 14103/2019

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-3/T-2 B. Sc. Engineering Examinations 2017-2018

Sub: IPE 303 (Product Design I)

Full Marks : 210 Time : 3 Hours

The figures in the margin indicate full marks.



Shigley's Mechanical Engineering Design Book will be supplied. Assume any missing data.

I. (a) A plane stress element has CTx = 9 MPa, CTy = -6 MPa and Txy = 3 MPacw.

(i) Draw a Mohr's circle diagram properly labeled

(ii) Find the principal normal and shear stresses

(iii) Determine the angle from the x axis to CT]

(iv) Draw stress elements and label all details.

(b) A utility hook ( a piece of metal or other hard material curved or bent back at an

angle, for catching hold of or hanging utilities on) was formed from a round rod of diameter

d = 18 mm into the geometry shown in Figure I(b). What are the stresses at the inner and

outer surfaces at section A-A if F = 3 kN, L = 240 mm, and D; = 60 mm?I - ._~~-_-t'~_k '...._/-.("-.£:--f-

(20)

(15)

Figure-l (b)

2. (a) Superposition theorem resolves the effect of combined loading on a structure by

determining the effects of each load separately and adding the results algebraically. Using

superposition, find the deflection of the steel shaft at A in the Figure 2(a). Find the

deflection at midspan.J3~ what percentage do these two values differ? (20)y

-15 in -'->'-1 '. 24in~~~I

340lbf

ISO Ihf/ft

A1.5 In-dia. shail

Figure-2(a) ~'Cc

(b) A cantilever beam ACB supports two concentrated loads PI and P2, as shown in the

Figure 2(b). Using Castigliano's theorem, determine the deflections 0e and 0B at points C

and B, respectively.

Contd P12

(15)

(0

... .'

=2=

IPE 303Conld ... Q. No. 2(b)

Figure,2(b)

3. (a) A helical compression spring is to be made of oil-tempered wire of 4-mm diameterwith a spring index of C = 10. The spring is to operate inside a hole, so buckling is not aproblem and the ends can be left plain. The free length of the spring should be 80 mm. A

force of 50 N should deflect the spring 15 mm. (25)(i) Determine the spring rate.(ii) Determine the minimum hole diameter for the spring to operate in.(iii) Determine the total number of coils needed.(iv) Determine the solid length.(v) Determine a static factor of safety based on the yielding of the spring if it iscompressed to its solid length.

(b) Task: Design of Axially Loaded Thick Plate with a Hole and Fillets (Figure 3(b». Afilleted plate of thickness I supports an axial load P. Determine the radius,. of the fillets

so that the same stress occurs at the hole and the fillets. (10)Given: P = 50 kN, D = 100 mm, df= 66 mm, dh = 20 mm, I = 10 mm.

Design Decisions: The plate will be made of a relatively brittle metallic alloy, so youshould consider stress concentration.

0"" Figure,3(b)

4. (a) A 'ductile hot-rolled steel bar has a minImum yield strength in tension andcompression of 350 MPa. Using the distortion-energy and maximum-shear-stress

theories, determine the factors of safety for the plane stress state erA = 100 MPa and

~=~OMPa. (1~(b) A cylinder subjected to internal pressure Pi has an outer diameter of 14 in and a I-in wall

thickness. For the cylinder material, K1c = 72 kpsi ..ji;; , Sy = 170 kpsi, and Sut = 192 kpsi.

If the cylinder contains a radial crack in the longitudinal direction of depth 0.5 1D,

determine the pressure that will cause uncontrollable crack growth. (20)

Contd P/3

=3=IrE 303


5. (a) Discuss the 'Specification Development' phase of the product design process for a

company planning to launch a new model of motorbike. (10)(b) Explain Function, Sub-function and Constraint, using a food processor as an example. (10)(c) Explain the generic product development process. Show the development phases

including some of the typical tasks and responsibilities of the key business functions for

each phase. (15)

6. (a) The basic quality function deployment methodology involves four basic phases.

Explain each phases with appropriate example. (10)(b) What are the variants of generic product development process? Provide their

description, distinct features and examples. (10)(c) Formulate torque transmission capacity equation of semi-centrifugal clutch with

necessary schematic diagrams. (15)

7. (a) Explain the 'FAST method' for functional decomposition. (10)(b) How do you classify product development projects? What types of competitive

strategy an organization can adopt to introduce new products to the market? (10)(c) A solid round bar with diameter of2 in has a groove cut to a diameter of 1.8 in, with a

radius of 0.1 in. The bar is not rotating. The bar is loaded with a repeated bending load

that causes the bending moment at the groove to fluctuate between 0 and 25000 lbf-in.

The bar is hot-rolled AISI 1095, but the groove has been machined. Determine the factor

of safety for fatigue based on infinite life using the modified Goodman criterion, and the

factor of safety for yielding. (15)

8. (a) What are the steps for subtract and operate procedure? Draw a function tree for a

vacuum cleaner using subtract and operate procedure and explain.

(b) The rotating solid steel shaft shown in the Figure 8(b) is simply supported by bearings

at points B and C and is driven by a gear (not shown) which meshes with the spur gear at

D, which has a l50-mm pitch diameter. The force F from the drive gear acts at a pressure

angle of 20°. The shaft transmits a torque to point A of TA = 340 N-m. The shaft is

machined. from steel with Sy = 420 MPa and SUI = 560 MPa. Using a factor of safety of

2.5, determine the minimum allowable diameter of the 250 mm section of the shaft based

on (i) a static yield analysis using the distortion energy theory and (ii) a fatigue-failure

analysis. Assume sharp fillet radii at the bearing shoulders for estimating stress-

concentration factors.

Contd P/4

(10)

(15)

".'

=4=IPE 303

. Contd ... Q. No. S(b)

I

I

I

I

'-IOOmm. """

Figure 8 (b)

(c) The shaft shown in the Figure 8(c) is machined from AISI 1040 CD steel. The shaft

rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are

F, = 2500 Ibf and F2 = 1000 Ibf. Determine the minimum fatigue factor of safety based

on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to

failure. Also check for yielding. (10)

. I

I!

1. in J2

B

F2

•8 in

All fillets ~ in R.

•

--- .••..4--~-10in

I~in8

~8in ..I.

Figure 8(c)

FOUR THREE.

Documents

Transcript of FOUR THREE.