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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Structural EngineeringStructural Engineering
Sergio F. BreñaSergio F. Breña
STEM Education InstituteSTEM Education InstituteSaturday WorkshopSaturday WorkshopSeptember 30, 2006September 30, 2006
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
OutlineOutline
• 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 Some Definitions of Important Structural PropertiesProperties
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Structural EngineeringStructural Engineering
• What does a Structural Engineer do?What does a Structural Engineer do?
– A Structural Engineer designs the structural A Structural Engineer designs the structural systems and structural elements in buildings, systems and structural elements in buildings, bridges, stadiums, tunnels, and other civil bridges, stadiums, tunnels, and other civil engineering works (bones)engineering works (bones)
– Design: process of determining location, material, Design: process of determining location, material, and size of structural elements to resist forces and size of structural elements to resist forces acting in a structureacting in a structure
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Engineering Design ProcessEngineering Design Process
• Identify the problem (challenge)Identify the problem (challenge)• Explore alternative solutionsExplore alternative solutions
– Research past experienceResearch past experience– BrainstormBrainstorm– Preliminary design of most promising solutionsPreliminary 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 testsExperimental testing (prototype) or field tests– Peer evaluationPeer evaluation
• Build solution using available resources (materials, Build solution using available resources (materials, equipment, labor)equipment, labor)
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Design Process in Structural EngineeringDesign Process in Structural Engineering
• Select material for constructionSelect material for construction
• Determine appropriate structural system for a Determine appropriate structural system for a particular caseparticular case
• Determine forces acting on a structureDetermine forces acting on a structure
• Calculate size of members and connections Calculate size of members and connections to avoid failure (collapse) or excessive to avoid failure (collapse) or excessive deformationdeformation
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Examples of Typical StructuresExamples of Typical Structures
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Forces in StructuresForces in Structures
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Forces Acting in StructuresForces Acting in Structures
• Forces induced by gravityForces induced by gravity– Dead Loads (permanent): self-weight of structure Dead Loads (permanent): self-weight of structure
and attachmentsand attachments– Live Loads (transient): moving loads (e.g. Live Loads (transient): moving loads (e.g.
occupants, vehicles)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 AmherstUniversity of Massachusetts Amherst
Forces Acting in StructuresForces Acting in Structures
Vertical: Gravity Lateral: Wind, Earthquake
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Global StabilityGlobal Stability
Sliding Overturning
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Forces in Structural ElementsForces in Structural Elements
100 lb
Compression
100 lb
Tension
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Forces in Structural Elements (cont.)Forces in Structural Elements (cont.)
100 lb
Bending
Torsion
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Typical Structural Systems (1)Typical Structural Systems (1)
Arch
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Typical Structural Systems (2)Typical Structural Systems (2)
TrussC
T
CCT
Forces in Truss Members
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Typical Structural Systems (3)Typical Structural Systems (3)
Frame
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Typical Structural Systems (4)Typical Structural Systems (4)
Flat Plate
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Typical Structural Systems (5)Typical Structural Systems (5)
Folded Plate
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Typical Structural Systems (6)Typical Structural Systems (6)
Shells
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Properties of Civil Engineering MaterialsProperties of Civil Engineering Materials
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Definition of StressDefinition of Stress
Section X
T
T
Section X
Stress = Force/Area
T
Example (English Units):
T = 1,000 lb (1 kip)A = 10 in2.
Stress = 1,000/10 = 100 lb/in2
Example (SI Units):
1 lb = 4.448 N (Newton)1 in = 25.4 mm
T = 1,000 lb x 4.448 N/lb = 4448 NA = 10 in2 x (25.4 mm)2 = 6450 mm2
(1 in)2
Stress = 4448/6450 = 0.69 N/mm2
(MPa)
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Definition of StrainDefinition of Strain
L
T
T
Lo
Strain = L / Lo
Example:
Lo = 10 in.L = 0.12 in.
Strain = 0.12 / 10 = 0.012 in./in.
Strain is dimensionless!!(same in English or SI units)
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Stress – Strain Behavior of Elastic Mats.Stress – Strain Behavior of Elastic Mats.
Stress
Strain
E
E = Modulus of Elasticity = Stress / Strain
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Types of Stress-Strain BehaviorTypes of Stress-Strain BehaviorStress
Strain
E
(a) Linear Elastic
Stress
Strain(b) Non-linear Elastic
Stress
Strain(c) Elastic-plastic
Stress
Strain(d) Non-linear Plastic
Plastic strain Plastic strain
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Materials Used in Civil EngineeringMaterials Used in Civil Engineering
• Stone and MasonryStone and Masonry
• MetalsMetals– Cast IronCast Iron– SteelSteel– AluminumAluminum
• ConcreteConcrete
• WoodWood
• Fiber-Reinforced PlasticsFiber-Reinforced Plastics
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Engineering Properties of MaterialsEngineering Properties of Materials
• SteelSteel– Maximum stress: 40,000 – 120,000 lb/inMaximum stress: 40,000 – 120,000 lb/in22
– Maximum strain: 0.2 – 0.4Maximum strain: 0.2 – 0.4– Modulus of elasticity: 29,000,000 lb/inModulus of elasticity: 29,000,000 lb/in22
• ConcreteConcrete– Maximum stress: 4,000 – 12,000 lb/inMaximum stress: 4,000 – 12,000 lb/in22
– Maximum strain: 0.004Maximum strain: 0.004– Modulus of elasticity: 3,600,000 – 6,200,000 lb/inModulus of elasticity: 3,600,000 – 6,200,000 lb/in22
• WoodWoodValues depend on wood grade. Below are some samplesValues depend on wood grade. Below are some samples– Tension stress: 1300 lb/inTension stress: 1300 lb/in22
– Compression stress: 1500 lb/inCompression stress: 1500 lb/in22
– Modulus of elasticity: 1,600,000 lb/inModulus of elasticity: 1,600,000 lb/in22
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Concrete ComponentsConcrete Components
• Sand (Fine Aggregate)Sand (Fine Aggregate)• Gravel (Coarse Aggregate)Gravel (Coarse Aggregate)• Cement (Binder)Cement (Binder)• WaterWater• Air Air
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Fiber-Reinforced CompositesFiber-Reinforced Composites
PolymerMatrix
Polyester
Epoxy
Vinylester
Fiber Materials
Glass
Aramid (Kevlar)
CarbonFunction 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 AmherstUniversity of Massachusetts Amherst
Important Structural PropertiesImportant Structural Properties
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Engineering Properties of Structural ElementsEngineering Properties of Structural Elements
• StrengthStrength– Ability to withstand a given stress without failureAbility to withstand a given stress without failure
• Depends on type of material and type of force (tension or Depends on type of material and type of force (tension or compression)compression)
Tensile Failure Compressive Failure
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Engineering Properties of Structural ElementsEngineering Properties of Structural Elements
• Stiffness (Rigidity)Stiffness (Rigidity)
– Property related to deformationProperty related to deformation
– Stiffer structural elements deform less under the same Stiffer structural elements deform less under the same applied loadapplied load
– Stiffness depends on type of material (E), structural shape, Stiffness depends on type of material (E), structural shape, and structural configurationand structural configuration
– Two main typesTwo main types• Axial stiffnessAxial stiffness
• Bending stiffnessBending stiffness
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Axial StiffnessAxial Stiffness
L
T
T
Lo
Stiffness = T / L
Example:
T = 100 lbL = 0.12 in.
Stiffness = 100 lb / 0.12 in. = 833 lb/in.
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Bending StiffnessBending Stiffness
Stiffness = Force / Displacement
Example:
Force = 1,000 lbDisplacement = 0.5 in.
Stiffness = 1,000 lb / 0.5 in. = 2,000 lb/in.
Displacement
Force
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Stiffness of Different Structural ShapesStiffness of Different Structural Shapes
Stiffest
StifferStiff
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Types of Structural Elements – Bars and Types of Structural Elements – Bars and CablesCables
Bars can carry either tensionor compression Cables can only carry tension
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Types of Structural Elements – BeamsTypes of Structural Elements – Beams
Tension
Compression
Loads
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Providing Stability for Lateral LoadsProviding Stability for Lateral Loads
Racking Failure of Pinned Frame
Braced Frame Infilled Frame Rigid Joints
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Concepts in EquilibriumConcepts in Equilibrium
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Equilibrium of Forces (Statics)Equilibrium of Forces (Statics)
• Forces are a type of quantity called vectorsForces are a type of quantity called vectors– Defined by magnitude and directionDefined by magnitude and direction
• Statement of equilibriumStatement of equilibrium– Net force at a point in a structure = zero Net force at a point in a structure = zero
(summation of forces = zero)(summation of forces = zero)
• Net force at a point is determined using a Net force at a point is determined using a force polygon to account for magnitude and force polygon to account for magnitude and directiondirection
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Moment (Rotational) EquilibriumMoment (Rotational) Equilibrium
3 ft 6 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 AmherstUniversity of Massachusetts Amherst
Force Calculation in Simple StructureForce Calculation in Simple Structure
100 lb
8 ft
6 ft
10 ft
A
CB
36.9
Side BC
Side AB=
8 ft
6 ft=1.333
Side AC
Side AB=
10 ft
6 ft=1.667
Force BC =1.333Force AB
Force BC = 1.333 x 100 lb = 133.3 lb
Force AC =1.667Force AB
Force AC = 1.667 x 100 lb = 166.7 lb
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Graphic StaticsGraphic Statics
1 Square = 10 lb
100 lb
133.3 lb
166.7 lb
36.9
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Force Transfer from Beams to SupportsForce Transfer from Beams to Supports
Force, P
Span, L
1/3 L 2/3 L
2/3 P 1/3 P
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University of Massachusetts AmherstUniversity of Massachusetts Amherst
Force Transfer Example - BridgeForce Transfer Example - Bridge
8,000 lb 32,000 lb
22,000 lb* 18,000 lb**
L = 60 ft
30 ft 30 ft
15 ft 45 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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