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University of Massachusetts Amherst Structural Engineering Sergio F. Breña STEM Education Institute Saturday Workshop September 30, 2006

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University of Massachusetts Amherst Outline Introduction to Structural EngineeringIntroduction to Structural Engineering Forces in StructuresForces in Structures Structural SystemsStructural Systems Civil Engineering MaterialsCivil Engineering Materials Some Definitions of Important Structural PropertiesSome Definitions of Important Structural Properties

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University of Massachusetts Amherst Structural Engineering What does a Structural Engineer do?What does a Structural Engineer do? –A Structural Engineer designs the structural systems and structural elements in buildings, bridges, stadiums, tunnels, and other civil engineering works (bones) –Design: process of determining location, material, and size of structural elements to resist forces acting in a structure

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University of Massachusetts Amherst Engineering Design Process Identify the problem (challenge)Identify the problem (challenge) Explore alternative solutionsExplore alternative solutions –Research past experience –Brainstorm –Preliminary design of most promising solutions Analyze and design one or more viable solutionsAnalyze and design one or more viable solutions Testing and evaluation of solutionTesting and evaluation of solution –Experimental testing (prototype) or field tests –Peer evaluation Build solution using available resources (materials, equipment, labor)Build solution using available resources (materials, equipment, labor)

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University of Massachusetts Amherst Design Process in Structural Engineering Select material for constructionSelect material for construction Determine appropriate structural system for a particular caseDetermine appropriate structural system for a particular case Determine forces acting on a structureDetermine forces acting on a structure Calculate size of members and connections to avoid failure (collapse) or excessive deformationCalculate size of members and connections to avoid failure (collapse) or excessive deformation

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University of Massachusetts Amherst Examples of Typical Structures

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University of Massachusetts Amherst Forces in Structures

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University of Massachusetts Amherst Forces Acting in Structures Forces induced by gravityForces induced by gravity –Dead Loads (permanent): self-weight of structure and attachments –Live Loads (transient): moving loads (e.g. occupants, vehicles) Forces induced by windForces induced by wind Forces induced by earthquakesForces induced by earthquakes Forces induced by rain/snowForces induced by rain/snow Fluid pressuresFluid pressures OthersOthers

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University of Massachusetts Amherst Forces Acting in Structures Vertical: GravityLateral: Wind, Earthquake

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University of Massachusetts Amherst Global Stability SlidingOverturning

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University of Massachusetts Amherst Forces in Structural Elements 100 lb Compression 100 lb Tension

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University of Massachusetts Amherst Forces in Structural Elements (cont.) 100 lb Bending Torsion

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University of Massachusetts Amherst Typical Structural Systems (1) Arch

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University of Massachusetts Amherst Typical Structural Systems (2) Truss C T C C T Forces in Truss Members

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University of Massachusetts Amherst Typical Structural Systems (3) Frame

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University of Massachusetts Amherst Typical Structural Systems (4) Flat Plate

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University of Massachusetts Amherst Typical Structural Systems (5) Folded Plate

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University of Massachusetts Amherst Typical Structural Systems (6) Shells

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University of Massachusetts Amherst Properties of Civil Engineering Materials

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University of Massachusetts Amherst Definition of Stress Section X T T Stress = Force/Area T Example (English Units): T = 1,000 lb (1 kip) A = 10 in 2. Stress = 1,000/10 = 100 lb/in 2 Example (SI Units): 1 lb = N (Newton) 1 in = 25.4 mm T = 1,000 lb x N/lb = 4448 N A = 10 in 2 x (25.4 mm) 2 = 6450 mm 2 (1 in) 2 Stress = 4448/6450 = 0.69 N/mm 2 (MPa)

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University of Massachusetts Amherst Definition of Strain L T T Lo Strain = L / Lo Example: Lo = 10 in. L = 0.12 in. Strain = 0.12 / 10 = in./in. Strain is dimensionless!! (same in English or SI units)

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University of Massachusetts Amherst Stress – Strain Behavior of Elastic Mats. Stress Strain E E = Modulus of Elasticity = Stress / Strain

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University of Massachusetts Amherst Types of Stress-Strain Behavior Stress Strain E (a) Linear Elastic Stress Strain (b) Non-linear Elastic Stress Strain (c) Elastic-plastic Stress Strain (d) Non-linear Plastic Plastic strain

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University of Massachusetts Amherst Materials Used in Civil Engineering Stone and MasonryStone and Masonry MetalsMetals –Cast Iron –Steel –Aluminum ConcreteConcrete WoodWood Fiber-Reinforced PlasticsFiber-Reinforced Plastics

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University of Massachusetts Amherst Engineering Properties of Materials SteelSteel –Maximum stress: 40,000 – 120,000 lb/in 2 –Maximum strain: 0.2 – 0.4 –Modulus of elasticity: 29,000,000 lb/in 2 ConcreteConcrete –Maximum stress: 4,000 – 12,000 lb/in 2 –Maximum strain: –Modulus of elasticity: 3,600,000 – 6,200,000 lb/in 2 WoodWood Values depend on wood grade. Below are some samples –Tension stress: 1300 lb/in 2 –Compression stress: 1500 lb/in 2 –Modulus of elasticity: 1,600,000 lb/in 2

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University of Massachusetts Amherst Concrete Components Sand (Fine Aggregate)Sand (Fine Aggregate) Gravel (Coarse Aggregate)Gravel (Coarse Aggregate) Cement (Binder)Cement (Binder) WaterWater AirAir

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University of Massachusetts Amherst Fiber-Reinforced Composites Polymer Matrix Polyester Epoxy Vinylester Fiber Materials Glass Aramid (Kevlar) Carbon Function of fibers: Provide stiffness Tensile strength Functions of matrix: Force transfer to fibers Compressive strength Chemical protection Composite Laminate

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University of Massachusetts Amherst Important Structural Properties

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University of Massachusetts Amherst Engineering Properties of Structural Elements StrengthStrength –Ability to withstand a given stress without failure Depends on type of material and type of force (tension or compression)Depends on type of material and type of force (tension or compression) Tensile Failure Compressive Failure

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University of Massachusetts Amherst Engineering Properties of Structural Elements Stiffness (Rigidity)Stiffness (Rigidity) –Property related to deformation –Stiffer structural elements deform less under the same applied load –Stiffness depends on type of material (E), structural shape, and structural configuration –Two main types Axial stiffnessAxial stiffness Bending stiffnessBending stiffness

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University of Massachusetts Amherst Axial Stiffness L T T Lo Stiffness = T / L Example: T = 100 lb L = 0.12 in. Stiffness = 100 lb / 0.12 in. = 833 lb/in.

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University of Massachusetts Amherst Bending Stiffness Stiffness = Force / Displacement Example: Force = 1,000 lb Displacement = 0.5 in. Stiffness = 1,000 lb / 0.5 in. = 2,000 lb/in. Displacement Force

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University of Massachusetts Amherst Stiffness of Different Structural Shapes Stiffest Stiffer Stiff

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University of Massachusetts Amherst Types of Structural Elements – Bars and Cables Bars can carry either tension or compression Cables can only carry tension

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University of Massachusetts Amherst Types of Structural Elements – Beams Tension Compression Loads

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University of Massachusetts Amherst Providing Stability for Lateral Loads Racking Failure of Pinned Frame Braced Frame Infilled FrameRigid Joints

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University of Massachusetts Amherst Concepts in Equilibrium

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University of Massachusetts Amherst Equilibrium of Forces (Statics) Forces are a type of quantity called vectorsForces are a type of quantity called vectors –Defined by magnitude and direction Statement of equilibriumStatement of equilibrium –Net force at a point in a structure = zero (summation of forces = zero) Net force at a point is determined using a force polygon to account for magnitude and directionNet force at a point is determined using a force polygon to account for magnitude and direction

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University of Massachusetts Amherst Moment (Rotational) Equilibrium 3 ft6 ft A Moment of Force = Force x Distance To neutralize rotation about point A, moments from the two forces has to be equal and opposite: 100 lb x 3 ft = 50 lb x 6 ft

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University of Massachusetts Amherst Force Calculation in Simple Structure 100 lb 8 ft 6 ft 10 ft A C B 36.9 Side BC Side AB = 8 ft 6 ft =1.333 Side AC Side AB = 10 ft 6 ft =1.667 Force BC = Force AB Force BC = x 100 lb = lb Force AC = Force AB Force AC = x 100 lb = lb

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University of Massachusetts Amherst Graphic Statics 1 Square = 10 lb 100 lb lb lb 36.9

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University of Massachusetts Amherst Force Transfer from Beams to Supports Force, P Span, L 1/3 L2/3 L 2/3 P1/3 P

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University of Massachusetts Amherst Force Transfer Example - Bridge 8,000 lb32,000 lb 22,000 lb * 18,000 lb ** L = 60 ft 30 ft 15 ft45 ft *Front axle: 8,000 lb x 45/60 = 6,000 lb Rear axle: 32,000 lb x 30/60 = 16,000 lb **Front axle: 8,000 lb x 15/60 = 2,000 lb Rear axle: 32,000 lb x 30/60 = 16,000 lb

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University of Massachusetts Amherst

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