Individual Project IENG

8/10/2019 Individual Project IENG

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Individual Project Report

Prepared by

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IE 302 Section 001

Instructor: -----------------------------


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Introduction

The objective of the individual project is to learn how to use the software IDEAMAPS developed

in excel by ------------------ and ------------. The purpose of the software is to calculate a wide array of

values such as dimensions, area, material cost, penalty cost, processing cost, embodied energy, CO2

content, energy cost, and total cost (with energy) given the material properties, cross section shape, andmultiple shape parameters as inputs. The software is preprogrammed for six cross section shapes and

allows for new shapes to be added as inputs. For the individual project, only a square cross section and

I-beam cross section will be analyzed using three specified materials: steel, aluminum, and AISI 1040

Q&T - Oil. After obtaining the results from the software, the best material will be chose, and the

deflection and stress will be calculated for each cross section by hand.

Computer Results Square Cross Section

For the square cross section, no parameters were specified for the project, so the predefined

parameters were used for penalty costs, maximum deflection, beam length, maximum weight withoutpenalty, and penalty per pound over maximum limit. The inputs are given below:

Value Parameter Units

$0.000080 Penalty per MJ for energy intensity $/MJ

$0.0100 Penalty per pound for CO2 $/lbs

The support module was chosen to be a cantilever support, and the load module was chosen to be a

single point end load. The sketches are given below:

The addition parameters were not modified and will not be listed in this report. The final sketch of the

results and cross section will be provided in the next pages.


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Computer Results for Square Cross Section

Aluminum Steel AISI 1040 (Q&T - Oil)

Youngs Modulus (E) 10.00 30.00 29.00

Yield Strength (s) 30.00 50.00 72.50

Density (r) 0.100 0.280 0.280

Cost 2.00 1.00 2.40

Melting Point 900 1800 1779h (deflection constraint) 3.0488 2.3166 2.3363

h (strength constraint) 2.8845 2.4319 2.1495

Design Parameter 3.0488 2.4329 2.3363

Area 9.2951 5.9189 5.45820

Material Cost 111.54 99.44 222.43

Weight 55.77 99.44 92.68

Penalty Cost 25.77 69.44 62.68

Processing Cost 15.52 17.52 16.72

Total Cost w/o Energy 152.83 186.39 301.84

Embodied Energy 95.00 15.00 11.00

C02 12.00 2.10 2.10

Energy Cost 0.42 0.12 0.08CO2 Penalty Cost 6.69 2.09 1.95

Total Cost with Energy 159.95 188.60 303.86

The results for the computer calculations were verified using the design problem handout in class. For

this case, aluminum has a large cost advantage over both steel and AISI 1040. Although aluminum has

the largest cost advantage, steel and AISI provide a much smaller beam design, but the cost difference is

just too large to justify using steel or AISI 1040 unless the specific application requires a size constraint.

Therefore, aluminum is the best material for the loading specifications. The cost differences and final

design with the square cross section are given below:

Cost Differences Square Cross Section

Materials Cost Difference ($)

Aluminum and Steel 28.65

Steel and AISI 1040 115.26

Aluminum and AISI 1040 143.91

Figure 1 - Square cross section for aluminum. All units are in inches. The deflection constraint is used to determine the cross

section side length since the length for the deflection constraint satisfies both the deflection and strength constraint.


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Hand Calculations for Square Cross Section

Deflection Calculations

Known Values

Parameter Value

Youngs Modulus(E) 10 MpsiLength (L) 60

Point Load (P) 2000 lbs

Cross Section Side Length (X) 3.0488 inches

Deflection Max = (PL2)/(3EI) where I = L4/12 for a square cross section

Moment of Inertia (I) = 3.04884/12 = 7.2000

Deflection Max = (2000*603)/(3*10000000*7.2000)

Deflection Max = 2 inches

Stress Calculations

The stress will be calculated on the top surface of the base of the beam. This will be the point with the

maximum stress. There will be bending and shear stress.

Known Values

Parameter Value

Distance from Centroid to Surface (c) 1.5244 inches

Shear Force (V) 2000 lbs

Cross Section Area (A) 9.2951 inches

2

Moment of Inertia 7.2000 inches4

Bending Stress = Mc/I

Shear Stress = 3V/2A

M = PL = 2000*60 = 120000 lb-in

Where M is the moment, c is the distance from the center to the top surface, I is the moment of inertia,

V is the shear force (point load), A is the cross sectional area.

Bending Stress = (120000*1.5244)/7.2000 = 25406.67 psi = 25.41 ksi

Shear Stress = (3*2000)/(2*9.2951) = 322.751 psi = 0.321 ksi


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Computer Results I-Beam Cross Section

For the I-beam cross section, no parameters were specified for the project, so the predefined

parameters were used for penalty costs, maximum deflection, beam length, maximum weight without

penalty, and penalty per pound over maximum limit. The parameters different for the I-beam are given

below:

Value Parameter Units

$0.000080 Penalty per MJ for energy intensity $/MJ

$0.0100 Penalty per pound for CO2 $/lbs

The support module was chosen to be a cantilever support just as the square cross section, and the load

module was chosen to be a single point end load as well. The addition parameters were not modified

and will not be listed in this report. The final sketch of the results and cross section will be provided in

the next pages.

Computer Results for I-Beam

Aluminum Steel AISI 1040 (Q&TOil)

Youngs Modulus (E) 10.00 30.00 29.00

Yield Strength (s) 30.00 50.00 72.50Density (r) 0.100 0.280 0.28

Cost 2.00 1.00 2.40

Melting Point 900 1800 1779

h (deflection constraint) 1.8859 1.3426 1.3565

h (strength constraint) 2.1339 1.6907 1.4320

Design Parameter 2.1339 1.6907 1.4320

Area 3.0009 2.3361 1.94806

Material Cost 36.01 39.25 79.39

Weight 18.01 39.25 33.08

Penalty Cost 0.00 9.25 3.08

Processing Cost 23.43 25.95 21.63

Total Cost w/o Energy 59.44 74.44 104.10

Embodied Energy 95.00 15.00 11.00

C02 12.00 2.10 2.10

Energy Cost 0.14 0.05 0.03

CO2 Penalty Cost 2.16 0.82 0.69

Total Cost with Energy 61.73 75.31 104.82


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For this case, aluminum has a large cost advantage over both steel and AISI 1040 just as in the case with

the square cross section. Overall, the advantages in choosing aluminum over steel and AISI 1040 are

similar to the square cross section. The cost for aluminum is the lowest, but size is greater for aluminum

than for steel and AISI. Therefore, aluminum is the best material for the loading specifications based

on cost. The cost differences and final design with the I-beam cross section are given below:

Cost Differences I-Beam Cross Section

Materials Cost Difference ($)

Aluminum and Steel 13.58

Steel and AISI 1040 29.51

Aluminum and AISI 1040 43.09

Figure 2- I-beam cross section for aluminum. All units are in inches. The strength constraint is used to determine the height since

the length for the deflection constraint satisfies both the deflection and strength constraint.

Hand Calculations for I-beam Cross Section

Deflection Calculations

Known Values

Parameter Value

Youngs Modulus(E) 10 MpsiLength (L) 60 inches.85

Point Load (P) 2000 lbs

Cross Section Side Length (X) 3.0488 inches

Deflection Max = (PL3)/(3EI)

Moment of Inertia (I) = 0.525 inches4


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Deflection Max = (2000*603)/(3*10000000*0.525)

Deflection Max = 0.46 inches

Stress Calculations

The stress will be calculated on the top surface of the base of the beam. This will be the point with the

maximum stress. There will be bending and shear stress.

Known Values

Parameter Value

Distance from Centroid to Surface (c) 1.06695 inches

Shear Force (V) 2000 lbs

Cross Section Area Web (A) 0.652 inches2

Moment of Inertia 0.525 inches4

Bending Stress = Mc/I

Shear Stress = V/A

M = PL = 2000*60 = 120000 lb-in

Where M is the moment, c is the distance from the center to the top surface, I is the moment of inertia,

V is the shear force (point load), A is the cross sectional area of the web.

Bending Stress = (120000*1.0670)/0.525 = 243.87 ksi

Shear Stress = 2000/0.652= 3067.49 psi = 3.067 ksi

Conclusion

Overall, the software is simple to use and increases the time required for calculating a large number of

properties for a given material and loading situation. For the square cross section and the I-beam cross

section, the aluminum is the best material for the for the given parameters. The actual deflection and

stress were both calculated for the I-beam and square cross sections using aluminum as the material.

For both cross sections, the stress and deflection were both small compared to the modulus and the

length of the beam. The I-beam had a substantial cost and weight savings compared to the square cross

section. The savings are given in the table below:

Cost and Weight Savings Choosing I-Beam

Cost Savings $98.22

Weight Savings 37.76 lbs


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Individual Project IENG