two - Texas A&M Universityfaculty-legacy.arch.tamu.edu/anichols/index_files/... · Analysis 15 Lecture 2 Architectural Structures III ARCH 631 F2008abn Units measures ± US customary

1

F2009abn

two

structural analysis

(statics & mechanics)Analysis 1

Lecture 2

Applied Architectural Structures

ARCH 631

lecture

APPLIED ARCHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS

ARCH 631

DR. ANNE NICHOLS

FALL 2013

F2009abn

Structural Requirements

• serviceability

– strength

– deflections

• efficiency

– economy of materials

• construction

• cost

• other

Analysis 2

Lecture 2

Architectural Structures III

ARCH 631

www.pbs.org/wgbh/buildingbig/

Analysis 3

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Structure Requirements

• strength &

equilibrium

– safety

– stresses

not greater

than

strength

– adequate

foundation

Analysis 4

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• stability &

stiffness

– stability of

components

– minimum

deflection and

vibration

– adequate

foundation

2

Analysis 5

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• economy and

construction

– minimum material

– standard sized

members

– simple connections

and details

– maintenance

– fabrication/ erection


Analysis 6

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Relation to Architecture

“The geometry and arrangement of the load-bearing members, the use of materials, and the crafting of joints all represent opportunities for buildings to express themselves. The best buildings are not designed by architects who after resolving the formal and spatial issues, simply ask the structural engineer to make sure it doesn’t fall down.” - Onouy & Kane

Analysis 7

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• dead load

– static, fixed, includes

material weights, fixed

equipment

• live load

– transient and moving

loads (including

occupants)

• snow load

Structural Loads - STATIC

Analysis 8

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• wind loads

– dynamic, wind pressures

treated as lateral static

loads on walls, pressure

or suction

– pressure determined

from wind velocity, qh

– dynamic effects include

motion from buffeting or

“vortex shedding”

Structural Loads – STATIC & DYNAMIC

AqCF hdW

3

Analysis 9

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• earthquake loads

– seismic, movement of

ground (3D)

– building mass responds

– static models often used,

V is static shear

• impact loads

– rapid, energy loads

Structural Loads - DYNAMIC

WRZICWV

Analysis 10

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Dynamic Response

Analysis 11

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Dynamic Response

• period of vibration or

frequency

– wave

– sway/time period

• damping

– reduction in sway

• resonance

– amplification of sway

Analysis 12

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Statics & Mechanics Review

• how loads affect our structures

– statics: things don’t move

• forces

• supports & connections

• equilibrium

– mechanics: things can change shape

• stress & strain

• deflections

• buckling

4

Analysis 13

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Structural Math

• quantify environmental loads

– how big is it?

• evaluate geometry and angles

– where is it?

– what is the scale?

– what is the size in a particular direction?

• quantify what happens in the structure

– how big are the internal forces?

– how big should the beam be?

Analysis 14

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Physical Math

• physics takes observable phenomena

and relates the measurement with rules:

mathematical relationships

• need

– reference frame

– measure of length, mass, time, direction,

velocity, acceleration, work, heat,

electricity, light

– calculations & geometry

Analysis 15

Lecture 2


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Units

• measures

– US customary & SI

litergallonVolume

Temperature

Force

Mass

Length

Units

CF

N, kNlb force

g, kglb mass

mm, cm, min, ft, mi

SIUS

Analysis 16

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Vectors

• scalars – any quantity

• vectors - quantities with direction

– like displacements

– summation results in

the “straight line path”

from start to end

– normal vector is perpendicular to

something

y

xz

5

Analysis 17

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Forces & Reactions

• Newton’s 3rd law:

– for every force of action there is an equal and opposite reaction alongthe same line

• external forces act on bodies

– can cause moments

• internal forces are

– in bodies

– between bodies (connections)

Analysis 18

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Force Components

• convenient to resolve into 2 vectors

• at right angles

• in a “nice” coordinate system

• is between Fx and F from FxFy

Fx

F

x

y

Fy

Fx

F

Fy

Fx

FcosFFx

sinFFy

22

yx FFF

x

y

F

Ftan

Analysis 19

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Load Types

• weight (F = ma)

• concentrated

• distributed

– uniform

– linear

• friction

– F=N

tAW

x

x/2

W

x/2

x

2x/3

W/2

x/3

x

x/2

W

x/6 x/3

W/2

0

Wxw w w 22

Wxw

w

2w

Analysis 20

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Load Tracing

• tributary load

– think of water flow

– “concentrates” load of

area into center

widthtributaryarea

loadw

width

6

Analysis 21

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Moments

• defined by magnitude and direction

• units: Nm, kft

• direction:

+ ccw (right hand rule)

- cw

• value found from Fand distance

• d also called “lever” or “moment” arm

F

A

C

B

dFM

d

Analysis 22

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Equilibrium

• analytically

• free body diagrams

0 xx FR

0 yy FR

0MM

Analysis 23

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Free Body Diagram

• FBD (sketch)

• tool to see all forces on a body or a

point including

– external forces

– weights

– force reactions

– external moments

– moment reactions

– internal forces

Analysis 24

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Supports and Connections

7

Analysis 25

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Supports and Connections

Analysis 26

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Centroid

• “average” x & y of an area

• for a volume of constant thickness

– where is weight/volume

– center of gravity = centroid of area

A

Axx

A

Ayy

AtW

Analysis 27

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Moments of Inertia

• 2nd moment area

–math concept

– area x (distance)2

• need for behavior of

– beams

– columns

2

ycxx AdII

Analysis 28

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Internal and Pin Forces

– 3 equations per three-force body

– two-force body forces in line

– 2 reactions per pin + support forces

A

B

C

D

G

E F

Ax

Ay D

8

Analysis 29

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Internal Beam V & M (+P)

• maximums needed for design

• Mmax at V = 0

V

L

+

M+

-

L/2

L

+V

+M

Analysis 30

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Deflected Shape

• positive bending moment

– tension in bottom, compression in top

• negative bending moment

– tension in top, compression in bottom

• zero bending moment

– inflection point

Analysis 31

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Stress

• stress is a term for the intensity of a

force, like a pressure

• internal or applied

• force per unit area

A

Pstress

Analysis 32

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Stress Types

• normal stress is normal

to the cross section

• shear stress parallel

to a surface

A

Pf cort

td

P

A

Pfv

9

Analysis 33

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• bearing stress on a

surface by contact in

compression

• torsional stress by

shear from twisting

Stress Types

td

P

A

Pf p

J

Tfv

Analysis 34

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• single shear

• double shear

• bearing

Bolt Stresses

4

2dv

P

A

Pf

4

2

22

2 dv

P

A

P

A

Pf

td

P

A

Pf

projected

p

Analysis 35

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• tension and compressive stress caused

by bending

• shear stress from bending

Bending Stresses

S

M

I

Mcfb

Ib

VQf avev

Analysis 36

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• plates with

– nails

– rivets

– bolts

• splices

Connectors Resisting Shear

x

y

ya

4”

2”

2”

12”

8” p

p p

4.43”

I

VQ

p

V allongitudin

pI

VQnF

areaconnected

connector

10

Analysis 37

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Strain

• materials deform

• axially loaded materials change

length

• bending materials deflect

• STRAIN:

– change in length over length

L

Lstrain

Analysis 38

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Problem Solving

1. STATICS:

equilibrium of external forces,

internal forces, stresses

2. GEOMETRY:

cross section properties, deformations and

conditions of geometric fit, strains

3. MATERIAL PROPERTIES:

stress-strain relationship for each material

obtained from testing

Analysis 39

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Stress to Strain

• important to us in - diagrams:

– straight section

– LINEAR-ELASTIC

– recovers shape

(no permanent

deformation)

f

Ef

AE

PL

Analysis 40

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Behavior Types

• brittle

• semi-brittle

11

Analysis 41

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Plastic Behavior

• ductile

at yield stress

Analysis 42

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22

maxmax

f

A

Pf

o

v

• if we need to knowwhere max f and fv

happen:

Maximum Stresses

F

oA

Pf max1cos0

5.0sincos45

Analysis 43

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Thermal Deformation

• - the rate of strain per degree

• UNITS : ,

• length change:

• thermal strain:

– no stress when movement allowed

LTT

TT

F C

Analysis 44

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Beam Deflections

• curvature, R

allowableactualxy )(max

EI

M

R

1

dxEI

xMslope

)(

EI

xMcurvature

)(

dxEI

xMdeflection

)(

12

Analysis 45

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Column Stability

• short columns

• slenderness ratio = Le/r (L/d)

• radius of gyration =A

Ir

aactual

critical FA

Pf

weak axis

2

2

2

22

rL

E

LA

EAr

A

Pf

ee

criticalcritical

2

e

2

critical

rL

EAP

Analysis 46

Lecture 2


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Column Stresses

• when a column gets stubby, Fy will limit the

load

• real world has loads

with eccentricity

• end conditions LKLe

Documents

two - Texas A&M Universityfaculty-legacy.arch.tamu.edu/anichols/index_files/... · Analysis 15 Lecture 2 Architectural Structures III ARCH 631 F2008abn Units measures ± US customary