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 University of Massachusetts Amherst Overturning

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

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

Typical Structural Systems (1) Arch University of Massachusetts Amherst

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

Typical Structural Systems (3) Frame 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

Section X Definition of Stress T Stress = Force/Area Example (English Units): T = 1,000 lb (1 kip) A = 10 in 2 .

Section X Stress = 1,000/10 = 100 lb/in 2 T T 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 in 2 x (25.4 mm) 2 = 6450 mm 2 (1 in) 2 Stress = 4448/6450 = 0.69 N/mm 2 (MPa) University of Massachusetts Amherst

D L Lo T Definition of Strain Strain = D L / Lo Example: Lo = 10 in.

D L = 0.12 in.

Strain = 0.12 / 10 = 0.012 in./in.

Strain is dimensionless!!

(same in English or SI units) T University of Massachusetts Amherst

Stress Stress – Strain Behavior of Elastic Mats.

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

Stress Types of Stress-Strain Behavior Stress Stress E Strain (a) Linear Elastic Stress Strain (b) Non-linear Elastic Plastic strain (c) Elastic-plastic Strain Plastic strain Strain (d) Non-linear Plastic 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/in 2 – Maximum strain: 0.2 – 0.4

– Modulus of elasticity: 29,000,000 lb/in 2 • Concrete – Maximum stress: 4,000 – 12,000 lb/in 2 – Maximum strain: 0.004

– Modulus of elasticity: 3,600,000 – 6,200,000 lb/in 2 • Wood 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 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 Fiber Materials Glass Aramid (Kevlar) Carbon Function of fibers: •Provide stiffness •Tensile strength University of Massachusetts Amherst Polymer Matrix Polyester Epoxy Vinylester Functions of matrix: •Force transfer to fibers •Compressive strength •Chemical protection

Important Structural Properties University of Massachusetts Amherst

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 University of Massachusetts Amherst Compressive Failure

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

Axial Stiffness D L T Lo Stiffness = T / D L Example: T = 100 lb D L = 0.12 in.

Stiffness = 100 lb / 0.12 in. = 833 lb/in.

T University of Massachusetts Amherst

Force Displacement 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.

University of Massachusetts Amherst

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

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

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

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

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 (Rotational) Equilibrium 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 3 ft 6 ft University of Massachusetts Amherst

6 ft A B Force Calculation in Simple Structure Side BC Side AB = 8 ft 6 ft = 1.333

Side AC Side AB = 10 ft = 1.667

6 ft 36.9

 8 ft 100 lb C Force  Force  Force  BC AB = 1.333

BC = 1.333 x 100 lb = 133.3 lb Force  Force  AC AB = 1.667

Force  AC = 1.667 x 100 lb = 166.7 lb University of Massachusetts Amherst

Graphic Statics 100 lb 36.9

 133.3 lb University of Massachusetts Amherst 1 Square = 10 lb

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

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