Chapter 1 Introduction to Structural Mechanics

Chapter 1 Introduction to Chapter 1 Introduction to Structural MechanicsStructural Mechanics

Autumn 2008

Dr. Pizhong Qiao, P.E.

Department of Engineering Mechanics, Hohai University

a. Structures - Introductiona. Structures - IntroductionStructure – a physical entity has a unitary character that can be

conceived of as an organization of positioned constituent element in

space in which the character of the whole dominates the

interrelationship of the part.

• Primarily designed to function as a whole unit

• Secondarily as an array of discrete elements

• Function: Channeling the load to the support (ground)

Designing a structure – the act of positioning constituent elementsb. Primary Classification (Fig. 1-1)Method for classifying structural elements and systems:

• Shape (geometry: line-forming vs. surface-forming)

• Basic physical properties (stiffness: flexible vs. rigid)

• Others: 1) one- or two-way systems and 2) Materials

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c. Primary Structural Elementsc. Primary Structural Elements

Based on Stiffness (Fig. 1-3):

• Rigid element – beam, column or strut, tie-rod, arch, flat plate, singly-curved plate, and shell

• Flexible elements – cable (straight or draped) and membrane

• Derived elements – frame, truss, geodesic dome, net

d. Primary Structural Units and Aggregations

Building structures are volume-forming in nature

Bridge structures are used to form or support linear surface

• Structural unit – a discrete volume-forming structural element or an assembly of structural elements and usually consists of (Fig. 1-4)

• Horizontal spanning system

• Vertical support system

• Lateral support system

Rigid structures

Flexible Structures

One-way and two-way structures

Structural Assembly

e. Analysis and Design of Structures – Basic e. Analysis and Design of Structures – Basic IssuesIssuesFundamental Phenomena (Figs. 1-5, 1-6, 1-7):

• Overall stability

• Internal stability

• Strength and stiffness of constituent elements

Member under Internal Forces - the action of an external force on a structure produces internal forces within a structure (Fig. 1-8):

• Tension

• Compression

• Bending

• Torsion

• Bearing

Internal forces stress and strain

• Deflection (excessive deformation)

Structural Failures

Structural Stability

Member behaviors under loading

f. Funicular Structuref. Funicular StructureDefinition – structures with shapes where only a state of tension or

compression is induced by the loading (Fig. 1-9)

For example, an arch can be conceived of as an inverted catenary (Fig. 1-10)

• A tension funicular pulls inward and downward; a support or foundation must apply an outward and upward force on the structure

• A compression funicular moves outward and downward; a foundation must exert an inward and upward force on the structure

• The combinations of applied forces acting on the foundation are commonly called thrusts.

• The final or resultant direction of the thrusts is along the tangent to the slope of structure at the point where the funicular structure meets the support (bending is not present in the structure; all the internal forces are directed axially along the length of the member)

• Further evolution of the basic funicular shape into other forms (Fig. 1-12)

Tension Funicular Compression FunicularInverted

Typical Funicular Structures

St. Perter’s Dome, Rome: An inverted catenary

Funicular structures: Transformations derived from basic shapes

Funicular structures: Transformations derived from basic shapes

Pursuing a Career as a Structural Engineer (SE):

Professional Engineer (Structures I):- Building - Bridge- Foundation- Lateral Structures (wind or seismic)- Steel- Reinforced Concrete- Masonry- Timber

Professional Engineer (Structures II, CA):- Seismic Design- Earthquake Engineering

Structural Engineering Certification Board (SECB)

a. Mechanics – Applied Science dealing with forces and a. Mechanics – Applied Science dealing with forces and motionsmotionsEquilibrium – a system of forces acting on a body is in a state of balance

• Statics – relations between forces acting on rigid bodies that are in equilibrium and at rest

• Dynamics – rigid bodies in motion

• Mechanics (Strength) of Materials – relation between applied (external) force on a body and internal effects in the body

Structural Analysis and Design – use as tools from each of the above basic fields in a nonsequential manner and in an integrative way.

b. Forces and Moments- a directed interaction between bodies

- Scalar and Vector

- Graphics Statics – Parallelogram Law

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c. Reaction

d. Shear and Moment

e. Material Properties

eStructures - CD

Point of Inflection (P.I.):

1. Point of zero moment

2. Transition point between positive and negative moments

3. Point at where the reversal of curvature takes place.

Examples:

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a. Analysis and Design Criteriaa. Analysis and Design Criteria• Serviceability – safe design without excessive material distress and with

deformation within an acceptable range

• Efficiency – relatively economy (minimum volume)

• Construction – material used should be easy to fabricate and assemble

• Costs – material economy and ease of construction

• Others – Subjective matters (the role of Structure as a space definer)b. Design Philosophies- Allowable Stress Design (ASD)

- Plastic Design (PD)

- Load and Resistance Factor Design (LRFD)

c. Allowable Stress Design (ASD)- To ensure that the stress computed under the action of the working

load (i.e., service loads) of a structure do not exceed some predesigned allowable values.

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Rn – nominal resistance (psi or Pa)Qn – working or service stress (psi or Pa)i – type of load; m – number of load type

d. Plastic Design (PD)d. Plastic Design (PD)- To ensure that the factored load combinations of structure do not

exceed the maximum plastic strength of the structure

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Rn – nominal plastic strengthQn – nominal load effect – load factori – type of load; m – number of load type

e. Load and Resistance Factor Design (LRFD)- To ensure that the nominal resistance of the structure exceeds that of

the load effects. Two safety factors are used: one applied to the loads and the other to the resistance of the materials.

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Rn – nominal resistance of the structureQn –load effect – resistance factor (usually < 1.0) (Table 1.2)

i – type of load; m – number of load type – load factor (usually > 1.0) (Table 1.1)

e. Load and Resistance Factor Design (LRFD) (Cont.)- A satisfactory design is the one in which the probability of the structural

member exceeding a limit state (e.g., yielding, fracture or buckling etc) is minimal.

- The safety of the structural member is measured by a reliability or safety index (Fig. 1.24, Chen and Liu 1987)

- The magnitude of reflects the safety of the member (the larger of , the smaller the area of shaded area, and the more improbable that a limit state may be exceeded) = 3.0 for member and = 4.5 for connector under dead + live = 2.5 for member under dead + live + wind loading = 1.75 for member under dead + live + earthquake loading

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e. Load and Resistance Factor Design (LRFD) (Cont.)- Reliability or safety index (Fig. 1.24, Chen and Liu 1987)

- The magnitude of reflects the safety of the member (the larger of , the smaller the area of shaded area, and the more improbable that a limit state may be exceeded)

f. Serviceability Requirements- ASD, PD, and LRFD are related to the strength

- Excessively deflection is related to the stiffness of the structure

g. Loads on Structures- Classification of loads (Fig. 3-1)

- Dead load (Tables 3-1 and 3-2)

- Live load (Table 3-3)

- Wind loads (Figs. 3-2 and 3-3)

- Earthquake forces (Figs. 3-4 and 3-5)

h. Modeling the Structure- Types of connection and idealized models (Fig. 3-8)

Both must be satisfied in Design

- Transformation of the loading (see CD – eStructure)

i. Modeling the External loads

g. Loads on Structures

- Classification of loads (Fig. 3-1)

- Dead load (Tables 3-1 and 3-2) - Live load (Table 3-3)

g. Loads on Structures- Wind loads (Figs. 3-2 and 3-3)

g. Loads on Structures

- Earthquake forces (Figs. 3-4 and 3-5)

h. Modeling the Structures- Types of

connection and idealized models (Fig. 3-9)

a. Landmark Structures (Maumee River Bridge, Toledo, a. Landmark Structures (Maumee River Bridge, Toledo, Ohio)Ohio)

Design:

Single Pylon (with glass curtain wall)

Stainless steel clad cables

Concrete Box girder

Span (612 ft + 612 ft clearance spans)

a. Landmark Structures (Sunshine Skyway Bridge, Tampa, a. Landmark Structures (Sunshine Skyway Bridge, Tampa, FL)FL)

Design:Twin Pylons; 1200 ft cable-stayed main span with a single pylon; 175 ft vertical heightTotal length of 21,878 ft; Twin 40 ft. roadways

a. Landmark Structures (San Francisco-Oakland Bay a. Landmark Structures (San Francisco-Oakland Bay Bridge)Bridge)

Single tower (185 m + 385 m) (2007)

a. Landmark Structuresa. Landmark Structures

Truss frame design was selected(span: 235 + 510 + 235 m)

(Minato Oh-Hashi, Japan)

b. Structures (Bridges)b. Structures (Bridges)

Simple girder

Continuous girder

Gerber girder

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b. Structures (Buildings - Concrete)b. Structures (Buildings - Concrete)

b. Structures (Buildings – Timber or Steel)b. Structures (Buildings – Timber or Steel)

Timber construction

b. Structures (Buildings – Bracing)b. Structures (Buildings – Bracing)

Lateral system for bracing

Dome structures

c. Structure Faulty (wind engineering)c. Structure Faulty (wind engineering)

c. Structure Faulty (wind engineering)c. Structure Faulty (wind engineering)

Vortex-induced vibration

Great Belt Bridge

c. Structure Faulty (Connection or Joint Failure)c. Structure Faulty (Connection or Joint Failure)

d. Connectionsd. Connections

Weld connections

d. Connectionsd. Connections

Bolted frame beam connection

Bolted seated beam connection

Bolted stiffened seated beam connection

Bolted connections