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CIVIL ENGINEERING DISCIPLES Session 02 and 03 Subject: S0012 / Introduction to Civil Engineering Year: 2007

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Bina Nusantara

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Elasticity Unstressed Wire Apply Small Stress Remove Stress and Material Returns to Original Dimensions

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Bina Nusantara Unstressed Bottle Inelastic Material Properties Bottle Undergoing Compressive Stress Inelastic Response

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Bina Nusantara Compression Unstressed SpongeSponge in Compression

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Bina Nusantara Compressive Failure This paper tube was crushed, leaving an accordion-like failure Characteristic : depends on the cross-sectional area depends on the material depends on the length depends on the cross-sectional shape

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Bina Nusantara Tension Steel cables supporting I- Beams are in tension.

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Bina Nusantara Tensile Failure Frayed rope Most strands already failed Prior to catastrophic fail Characteristics : depends on the cross-sectional area depends on the material does not depend on the length does not depend on the cross- sectional shape

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Bina Nusantara Tensile Failure This magnesium test bar is tensile strained until fracture Machine characterizes the elastic response Data verifies manufacturing process control

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Bina Nusantara Force Direction Axial Stress on the Vertical Post Transverse Stress on the Horizontal Aluminum Rod

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Bina Nusantara Ductile Example Unstressed Coat Hangar After Applied Transverse Stress Beyond the Yield Stress Point

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Bina Nusantara Brittle Example Unstressed Stick Brittle Failure After Applied Stress Beyond the Yield Stress Point

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Bina Nusantara Moment of Inertia Quantifies the resistance to bending or buckling Function of the cross-sectional area Formulas can be found in literature Units are in length 4 (in 4 or mm 4 ) Symbol: I

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Bina Nusantara Moment of Inertia for Common Cross Sections Rectangle with height ‘h’ and length ‘b’ I = (in 4 or mm 4 ) Circle with radius ‘r’ I = (in 4 or mm 4 ) 2r b 12 bh 3 ____ 4 π r 4 h

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Bina Nusantara Modulus of Elasticity Quantifies a material’s resistance to deformation Constant for a material, independent of the material’s shape. Units are in force / area. (PSI or N/m 2 ) Symbol: E

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Bina Nusantara Flexural Rigidity Quantifies the stiffness of a material Higher flexural rigidity = stiffer material Product of the Modulus of Elasticity times the Moment of Inertia (E*I)

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Bina Nusantara Factor of Safety Designers make a bridge stronger than design target Factor of Safety = Most codes require minimum Factor of Safety > 1.6 Failure Level Actual Level

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Bina Nusantara Cross-Sections and Cross-Sectional Area

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Bina Nusantara Lever Concept Lever Relationship: F 1 * L 1 = F 2 * L 2 L1L1 L2L2 F1F1 F2F2

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Bina Nusantara Structural Analysis Structural analysis is a mathematical examination of a complex structure Analysis breaks a complex system down to individual component parts Uses geometry, trigonometry, algebra, and basic physics

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Bina Nusantara How Much Weight Can This Truss Bridge Support?

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Bina Nusantara Pythagorean Theorem In a right triangle, the length of the sides are related by the equation: a 2 + b 2 = c 2 a b c

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Bina Nusantara Sine (sin) of an Angle The angles are related to the lengths of the sides by the equations: sin θ 1 = = Opposite a Hypotenuse c sinθ 2 = = Opposite b Hypotenuse c a b c θ1θ1 θ2θ2

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Bina Nusantara Cosine (cos) of an Angle The angles are related to the lengths of the sides by the equations: cos θ 1 = = Adjacent b Hypoten use c cosθ 2 = = Adjacent a Hypotenuse c a b c θ1θ1 θ2θ2

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Bina Nusantara This Truss Bridge is Built from Right Triangles a b c θ1θ1 θ2θ2

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Bina Nusantara Vector Components Every vector can be broken into two parts, one vector with magnitude in the x-direction and one with magnitude in the y- direction. Determine these two components for structural analysis.

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Bina Nusantara Structural Analysis Problem Calculate the internal member forces on this nutcracker truss if the finger is pushing down with a force of eight newtons.

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