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Ken Youssefi/Thalia Anagnos Engineering 10, SJSU 1 Structures and Stiffness ENGR 10 Introduction to Engineering

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Ken Youssefi Engineering 10, SJSU 2 Wind Turbine Structure The support structure should be optimized for weight and stiffness (deflection) Support Structure The Goal

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Ken Youssefi Engineering 10, SJSU 3 Lattice structure Wind Turbine Structure Hollow tube with guy wire Hollow tapered tube

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Ken Youssefi Engineering 10, SJSU 4 Wind Turbine Structure Tube with guy wire and winch Tripod support Structural support

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Ken Youssefi Engineering 10, SJSU 5 Wind Turbine Structure World Trade Center in Bahrain Three giant wind turbine provides 15% of the power needed.

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Ken Youssefi Engineering 10, SJSU 6 Support structure failure, New York. Stress at the base of the support tower exceeding the strength of the material

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Ken Youssefi Engineering 10, SJSU 7 Support structure failure, Denmark. Caused by high wind

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Ken Youssefi Engineering 10, SJSU 8 Blade failure, Illinois. Failure at the thin section of the blade Lightning strike, Germany Support structure failure, UK

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Ken Youssefi Engineering 10, SJSU 9 Many different forms

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Engineering 10, SJSU 10 Cardboard Balsa wood PVC Pipe

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Ken Youssefi Engineering 10, SJSU 11 Foam Board Recycled Materials

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Engineering 10, SJSU 12 Metal Rods Old Toys

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Ken Youssefi Engineering 10, SJSU 13 Spring Stiffness F F ΔxΔx where k = spring constant Δ x = spring stretch F = applied force F = k ( Δ x) Compression spring Tension spring

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Ken Youssefi Engineering 10, SJSU 14 Stiffness (Spring) Deflection is proportional to load, F = k (x) Load (N or lb) Deflection (mm or in.) slope, k Slope of Load-Deflection curve: The Stiffness

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Ken Youssefi Engineering 10, SJSU 15 Stiffness (Solid Bar) Stiffness in tension and compression –Applied Forces F, length L, cross-sectional area, A, and material property, E (Youngs modulus) Stiffness for components in tension-compression E is constant for a given material E (steel) = 30 x 10 6 psi E (Al) = 10 x 10 6 psi E (concrete) = 3.4 x 10 3 psi E (Kevlar, plastic) = 19 x 10 3 psi E (rubber) = 100 psi F F L End view A F F L δ

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Ken Youssefi Engineering 10, SJSU 16 Stiffness Stiffness in bending –Think about what happens to the material as the beam bends How does the material resist the applied load? B Outer fibers (B) are in tension A Inner fibers (A) are in compression

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Ken Youssefi Engineering 10, SJSU 17 Stiffness of a Cantilever Beam Y = deflection = FL 3 / 3 EI F = force L = length Deflection of a Cantilever Beam Fixed end Support Fixed end Wind

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Ken Youssefi Engineering 10, SJSU 18 Concept of Area Moment of Inertia Y = deflection = FL 3 / 3 EI F = force L = length Deflection of a Cantilever Beam Fixed end Support The larger the area moment of inertia, the less a structure deflects (greater stiffness) Mathematically, the area moment of inertia appears in the denominator of the deflection equation, therefore; Fixed end Wind

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Clicker Question Ken Youssefi Engineering 10, SJSU 19 kg is a unit of force A)True B)False

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Clicker Question Ken Youssefi Engineering 10, SJSU 20 All 3 springs have the same initial length. Three springs are each loaded with the same force F. Which spring has the greatest stiffness? F F F K1K1 K2K2 K3K3 A.K 1 B.K 2 C.K 3 D.They are all the same E.I dont know

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Ken Youssefi Engineering 10, SJSU 21 Note: Intercept = 0 Default is: first column plots on x axis second column plots on y axis

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Ken Youssefi Engineering 10, SJSU 22 Concept of Area Moment of Inertia The Area Moment of Inertia, I, is a term used to describe the capacity of a cross-section (profile) to resist bending. It is always considered with respect to a reference axis, in the X or Y direction. It is a mathematical property of a section concerned with a surface area and how that area is distributed about the reference axis. The reference axis is usually a centroidal axis. The Area Moment of Inertia is an important parameter in determine the state of stress in a part (component, structure), the resistance to buckling, and the amount of deflection in a beam. The area moment of inertia allows you to tell how stiff a structure is.

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Ken Youssefi Engineering 10, SJSU 23 Mathematical Equation for Area Moment of Inertia I xx = (A i ) (y i ) 2 = A 1 (y 1 ) 2 + A 2 (y 2 ) 2 + …..A n (y n ) 2 A (total area) = A 1 + A 2 + ……..A n XX Area, A A1A1 A2A2 y1y1 y2y2

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Ken Youssefi Engineering 10, SJSU 24 Moment of Inertia – Comparison Load 2 x 8 beam Maximum distance of 1 inch to the centroid I1I1 I 2 > I 1, orientation 2 deflects less Maximum distance of 4 inch to the centroid I2I2 Same load and location 2 2 x 8 beam 4

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Ken Youssefi Engineering 10, SJSU 25 Moment of Inertia Equations for Selected Profiles (d) 4 64 I = Round solid section Rectangular solid section b h bh 3 1 I = 12 b h 1 I = 12 hb 3 d Round hollow section 64 I = [(d o ) 4 – (d i ) 4 ] dodo didi BH I = 12 bh Rectangular hollow section H B h b

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Ken Youssefi Engineering 10, SJSU 26 Show of Hands A designer is considering two cross sections as shown. Which will produce a stiffer structure? A.Solid section B.Hollow section C.I dont know 2.0 inch 1.0 inch hollow rectangular section 2.25 wide X 1.25 high X.125 thick H B h b B = 2.25, H = 1.25 b = 2.0, h = 1.0

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Ken Youssefi Engineering 10, SJSU 27 Example – Optimization for Weight & Stiffness Consider a solid rectangular section 2.0 inch wide by 1.0 high. I = (1/12)bh 3 = (1/12)(2)(1) 3 =.1667, Area = 2 ( )/(.1667) x 100=.20 = 20% less deflection ( )/(2) =.6 = 60% lighter Compare the weight of the two parts (same material and length), so only the cross sectional areas need to be compared. I = (1/12)bh 3 = (1/12)(2.25)(1.25) 3 – (1/12)(2)(1) 3 = =.1995 Area = 2.25x1.25 – 2x1 =.8125 So, for a slightly larger outside dimension section, 2.25x1.25 instead of 2 x 1, you can design a beam that is 20% stiffer and 60 % lighter Now, consider a hollow rectangular section 2.25 inch wide by 1.25 high by.125 thick. H B h b B = 2.25, H = 1.25 b = 2.0, h = 1.0

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Engineering 10, SJSU 28 Clicker Question Deflection (inch) Load (lbs) C B A The plot shows load versus deflection for three structures. Which is stiffest? A.A B.B C.C D.I dont know

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Ken Youssefi Engineering 10, SJSU 29 Stiffness Comparisons for Different sections SquareBox Rectangular Horizontal Rectangular Vertical Stiffness = slope

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Ken Youssefi Engineering 10, SJSU 30 Material and Stiffness E = Elasticity Module, a measure of material deformation under a load. Y = deflection = FL 3 / 3 EI F = force L = length The higher the value of E, the less a structure deflects (higher stiffness) Deflection of a Cantilever Beam Fixed end Support

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Ken Youssefi Engineering 10 - SJSU 31 Material Strength Standard Tensile Test Standard Specimen Ductile Steel (low carbon) S y – yield strength S u – fracture strength σ (stress) = Load / Area ε (strain) = (change in length) / (original length)

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Ken YoussefiEngineering 10 - SJSU 32 - the extent of plastic deformation that a material undergoes before fracture, measured as a percent elongation of a material. % elongation = (final length, at fracture – original length) / original length Ductility Common Mechanical Properties - the capacity of a material to absorb energy within the elastic zone (area under the stress-strain curve in the elastic zone) Resilience - the total capacity of a material to absorb energy without fracture (total area under the stress-strain curve) Toughness – the highest stress a material can withstand and still return exactly to its original size when unloaded. Yield Strength (S y ) - the greatest stress a material can withstand, fracture stress. Ultimate Strength (S u ) - the slope of the straight portion of the stress-strain curve. Modulus of elasticity (E)

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Ken Youssefi Engineering 10, SJSU 33 Modules of Elasticity (E) of Materials Steel is 3 times stiffer than Aluminum and 100 times stiffer than Plastics.

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Ken Youssefi Engineering 10, SJSU 34 Density of Materials Plastic is 7 times lighter than steel and 3 times lighter than aluminum. Plastics Aluminums Steel

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Impact of Structural Elements on Overall Stiffness Ken Youssefi / Thalia Anagnos Engineering 10, SJSU 35 Rectangle deforms Triangle rigid P P

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Clicker Question Ken Youssefi Engineering 10, SJSU 36 The higher the Modulus of Elasticity (E), the lower the stiffness A. True B. False

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Clicker Question Ken Youssefi Engineering 10, SJSU 37 Which of the following materials is the stiffest? A. Cast Iron B. Aluminum C. Polycarbonate D. Steel E. Fiberglass

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Clicker Question Ken Youssefi Engineering 10, SJSU 38 The applied load affects the stiffness of a structure. A. True B. False

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Ken Youssefi Engineering 10, SJSU 39 Stiffness Testing

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Ken Youssefi Engineering 10, SJSU 40 weights Load pulling on tower Dial gage to measure deflection Successful testers Stiffness Testing Apparatus

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