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**Structural Engineering**

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

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**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

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**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

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**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

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**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

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**Examples of Typical Structures**

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**University of Massachusetts Amherst**

Forces in Structures University of Massachusetts Amherst

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**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

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**Forces Acting in Structures**

Vertical: Gravity Lateral: Wind, Earthquake University of Massachusetts Amherst

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**University of Massachusetts Amherst**

Global Stability Sliding Overturning University of Massachusetts Amherst

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**Forces in Structural Elements**

100 lb Compression 100 lb Tension University of Massachusetts Amherst

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**Forces in Structural Elements (cont.)**

100 lb Bending Torsion University of Massachusetts Amherst

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**Typical Structural Systems (1)**

Arch University of Massachusetts Amherst

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**Typical Structural Systems (2)**

Truss C T Forces in Truss Members University of Massachusetts Amherst

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**Typical Structural Systems (3)**

Frame University of Massachusetts Amherst

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**Typical Structural Systems (4)**

Flat Plate University of Massachusetts Amherst

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**Typical Structural Systems (5)**

Folded Plate University of Massachusetts Amherst

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**Typical Structural Systems (6)**

Shells University of Massachusetts Amherst

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**Properties of Civil Engineering Materials**

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**University of Massachusetts Amherst**

Definition of Stress Section X 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 = N (Newton) 1 in = 25.4 mm T = 1,000 lb x 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 Stress = Force/Area T University of Massachusetts Amherst

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**University of Massachusetts Amherst**

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

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**Stress – Strain Behavior of Elastic Mats.**

E = Modulus of Elasticity = Stress / Strain Strain University of Massachusetts Amherst

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**Types of Stress-Strain Behavior**

(a) Linear Elastic (b) Non-linear Elastic (c) Elastic-plastic (d) Non-linear Plastic Plastic strain University of Massachusetts Amherst

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**Materials Used in Civil Engineering**

Stone and Masonry Metals Cast Iron Steel Aluminum Concrete Wood Fiber-Reinforced Plastics University of Massachusetts Amherst

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**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

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**University of Massachusetts Amherst**

Concrete Components Sand (Fine Aggregate) Gravel (Coarse Aggregate) Cement (Binder) Water Air University of Massachusetts Amherst

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**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

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**Important Structural Properties**

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**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) Tensile Failure Compressive Failure University of Massachusetts Amherst

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**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

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**University of Massachusetts Amherst**

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

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**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

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**Stiffness of Different Structural Shapes**

Stiffest Stiffer University of Massachusetts Amherst

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**Types of Structural Elements – Bars and Cables**

Bars can carry either tension or compression Cables can only carry tension University of Massachusetts Amherst

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**Types of Structural Elements – Beams**

Loads Tension Compression University of Massachusetts Amherst

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**Providing Stability for Lateral Loads**

Racking Failure of Pinned Frame Braced Frame Infilled Frame Rigid Joints University of Massachusetts Amherst

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**Concepts in Equilibrium**

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**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

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**Moment (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 University of Massachusetts Amherst

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**Force Calculation in Simple Structure**

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

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**University of Massachusetts Amherst**

Graphic Statics 1 Square = 10 lb 100 lb 133.3 lb 166.7 lb 36.9 University of Massachusetts Amherst

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**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

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**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

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**University of Massachusetts Amherst**

University of Massachusetts Amherst

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