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

Bina Nusantara

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

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

Bina Nusantara Compression Unstressed SpongeSponge in Compression

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

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

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

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

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

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

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

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

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

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

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)

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

Bina Nusantara Cross-Sections and Cross-Sectional Area

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

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

Bina Nusantara How Much Weight Can This Truss Bridge Support?

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

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

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

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

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.

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.