Structural Engineering

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## Structural Engineering

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**Structural Engineering**Sergio F. Breña STEM Education Institute Saturday Workshop September 30, 2006 University of Massachusetts Amherst**Outline**• Introduction to Structural Engineering • Forces in Structures • Structural Systems • Civil Engineering Materials • Some Definitions of Important Structural Properties University of Massachusetts Amherst**Structural Engineering**• 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 University of Massachusetts Amherst**Engineering Design Process**• Identify the problem (challenge) • Explore alternative solutions • Research past experience • Brainstorm • Preliminary design of most promising solutions • Analyze and design one or more viable solutions • Testing and evaluation of solution • Experimental testing (prototype) or field tests • Peer evaluation • Build solution using available resources (materials, equipment, labor) University of Massachusetts Amherst**Design Process in Structural Engineering**• Select material for construction • Determine appropriate structural system for a particular case • Determine forces acting on a structure • Calculate size of members and connections to avoid failure (collapse) or excessive deformation University of Massachusetts Amherst**Examples of Typical Structures**University of Massachusetts Amherst**Forces in Structures**University of Massachusetts Amherst**Forces Acting in Structures**• Forces induced by gravity • Dead Loads (permanent): self-weight of structure and attachments • Live Loads (transient): moving loads (e.g. occupants, vehicles) • Forces induced by wind • Forces induced by earthquakes • Forces induced by rain/snow • Fluid pressures • Others University of Massachusetts Amherst**Forces Acting in Structures**Vertical: Gravity Lateral: Wind, Earthquake University of Massachusetts Amherst**Global Stability**Sliding Overturning University of Massachusetts Amherst**100**lb Compression Forces in Structural Elements 100 lb Tension University of Massachusetts Amherst**100**lb Bending Forces in Structural Elements (cont.) Torsion University of Massachusetts Amherst**Arch**Typical Structural Systems (1) University of Massachusetts Amherst**C**T C C T Forces in Truss Members Typical Structural Systems (2) Truss University of Massachusetts Amherst**Frame**Typical Structural Systems (3) University of Massachusetts Amherst**Typical Structural Systems (4)**Flat Plate University of Massachusetts Amherst**Typical Structural Systems (5)**Folded Plate University of Massachusetts Amherst**Typical Structural Systems (6)**Shells University of Massachusetts Amherst**Properties of Civil Engineering Materials**University of Massachusetts Amherst**T**Example (English Units): T = 1,000 lb (1 kip) A = 10 in2. Stress = 1,000/10 = 100 lb/in2 Stress = Force/Area Section X Example (SI Units): 1 lb = 4.448 N (Newton) 1 in = 25.4 mm T = 1,000 lb x 4.448 N/lb = 4448 N A = 10 in2 x (25.4 mm)2 = 6450 mm2 (1 in)2 Stress = 4448/6450 = 0.69 N/mm2 (MPa) Section X T T Definition of Stress University of Massachusetts Amherst**T**DL Lo T Definition of Strain Strain = DL / Lo Example: Lo = 10 in. DL = 0.12 in. Strain = 0.12 / 10 = 0.012 in./in. Strain is dimensionless!! (same in English or SI units) University of Massachusetts Amherst**Stress – Strain Behavior of Elastic Mats.**Stress E E = Modulus of Elasticity = Stress / Strain Strain University of Massachusetts Amherst**Stress**Stress E Strain Strain Stress (a) Linear Elastic Stress (b) Non-linear Elastic Strain Strain Plastic strain Plastic strain (c) Elastic-plastic (d) Non-linear Plastic Types of Stress-Strain Behavior University of Massachusetts Amherst**Materials Used in Civil Engineering**• Stone and Masonry • Metals • Cast Iron • Steel • Aluminum • Concrete • Wood • Fiber-Reinforced Plastics University of Massachusetts Amherst**Engineering Properties of Materials**• Steel • Maximum stress: 40,000 – 120,000 lb/in2 • Maximum strain: 0.2 – 0.4 • Modulus of elasticity: 29,000,000 lb/in2 • Concrete • Maximum stress: 4,000 – 12,000 lb/in2 • Maximum strain: 0.004 • Modulus of elasticity: 3,600,000 – 6,200,000 lb/in2 • Wood Values depend on wood grade. Below are some samples • Tension stress: 1300 lb/in2 • Compression stress: 1500 lb/in2 • Modulus of elasticity: 1,600,000 lb/in2 University of Massachusetts Amherst**Concrete Components**• Sand (Fine Aggregate) • Gravel (Coarse Aggregate) • Cement (Binder) • Water • Air University of Massachusetts Amherst**Fiber-Reinforced Composites**Composite Laminate Polyester Polymer Matrix Epoxy Vinylester Glass • Functions of matrix: • Force transfer to fibers • Compressive strength • Chemical protection Fiber Materials Aramid (Kevlar) Carbon • Function of fibers: • Provide stiffness • Tensile strength University of Massachusetts Amherst**Important Structural Properties**University of Massachusetts Amherst**Compressive Failure**Tensile Failure Engineering Properties of Structural Elements • Strength • Ability to withstand a given stress without failure • Depends on type of material and type of force (tension or compression) University of Massachusetts Amherst**Engineering Properties of Structural Elements**• 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 stiffness • Bending stiffness University of Massachusetts Amherst**T**DL Lo T Axial Stiffness Stiffness = T / DL Example: T = 100 lb DL = 0.12 in. Stiffness = 100 lb / 0.12 in. = 833 lb/in. University of Massachusetts Amherst**Bending Stiffness**Displacement Force Stiffness = Force / Displacement Example: Force = 1,000 lb Displacement = 0.5 in. Stiffness = 1,000 lb / 0.5 in. = 2,000 lb/in. University of Massachusetts Amherst**Stiffest**Stiffness of Different Structural Shapes Stiff Stiffer University of Massachusetts Amherst**Types of Structural Elements – Bars and Cables**Bars can carry either tension or compression Cables can only carry tension University of Massachusetts Amherst**Loads**Compression Tension Types of Structural Elements – Beams University of Massachusetts Amherst**Racking Failure of Pinned Frame**Infilled Frame Rigid Joints Braced Frame Providing Stability for Lateral Loads University of Massachusetts Amherst**Concepts in Equilibrium**University of Massachusetts Amherst**Equilibrium of Forces (Statics)**• Forces are a type of quantity called vectors • Defined by magnitude and direction • Statement 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 direction University of Massachusetts Amherst**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 A 3 ft 6 ft Moment (Rotational) Equilibrium University of Massachusetts Amherst**8 ft**10 ft Side AC Side BC = = = = 1.667 1.333 100 lb 6 ft 6 ft Side AB Side AB A 10 ft 6 ft Force BC Force AC 1.333 1.667 = = Force AB Force AB C B Force AC = 1.667 x 100 lb = 166.7 lb Force BC = 1.333 x 100 lb = 133.3 lb 8 ft Force Calculation in Simple Structure 36.9 University of Massachusetts Amherst**166.7 lb**100 lb 36.9 133.3 lb 1 Square = 10 lb Graphic Statics University of Massachusetts Amherst**Force Transfer from Beams to Supports**Force, P 1/3 L 2/3 L 2/3 P 1/3 P Span, L University of Massachusetts Amherst**Force Transfer Example - Bridge**8,000 lb 32,000 lb 15 ft 45 ft 30 ft 30 ft L = 60 ft 22,000 lb* 18,000 lb** *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 University of Massachusetts Amherst**www.teachersdomain.org**University of Massachusetts Amherst