structural analysis (statics & mechanics)faculty.arch.tamu.edu/.../lectures-631-fall/Files/lect2_ygyIjjK.pdfAnalysis 1 F2018abn Lecture 2 Applied Architectural Structures ARCH 631

F2018abnAnalysis 1

Lecture 2

Applied Architectural Structures

ARCH 631

two

structural analysis

(statics & mechanics)

lecture

APPLIED ACHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

DR. ANNE NICHOLS

FALL 2018

F2018abnAnalysis 2

Lecture 2


ARCH 631

Structural Requirements

• strength

• serviceability

– deflections

• efficiency

– economy of materials

• construction

• cost

• other

www.pbs.org/wgbh/buildingbig/

F2018abnAnalysis 3

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Structure Requirements

• strength &

equilibrium

– safety

– stresses

not greater

than

strength

– adequate

foundation

F2018abnAnalysis 4

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• stability &

stiffness

– stability of

components

– minimum

deflection and

vibration

– adequate

foundation

F2018abnAnalysis 5

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• economy and

construction

– minimum material

– standard sized

members

– simple connections

and details

– maintenance

– fabrication/ erection


F2018abnAnalysis 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

F2018abnAnalysis 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

F2018abn

W d hF C q A

• 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”

Analysis 8

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Structural Loads – STATIC & DYNAMIC

F2018abn

W

ZICWVR

• earthquake loads

– seismic, movement of

ground (3D)

– building mass responds

– static models often used,

V is static shear

• impact loads

– rapid, energy loads

Analysis 9

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Structural Loads - DYNAMIC

F2018abnAnalysis 10

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Dynamic Response

F2018abnAnalysis 11

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Dynamic Response

• period of vibration or

frequency

– wave

– sway/time period

• damping

– reduction in sway

• resonance

– amplification of sway

F2018abnAnalysis 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

F2018abnAnalysis 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?

F2018abnAnalysis 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

F2018abnAnalysis 15

Lecture 2


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Units

• measures

– US customary & SI

Units US SI

Length in, ft, mi mm, cm, m

Volume gallon liter

Mass lb mass g, kg

Force lb force N, kN

Temperature F C

F2018abnAnalysis 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

F2018abnAnalysis 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)

http://www.physics.umd.edu

F2018abn

• convenient to resolve into 2 vectors

• at right angles

• in a “nice” coordinate system

• is between Fx and F from Fx

tany

x

F

F

2 2

x yF F F

sinyF F

cosxF F

Analysis 18

Lecture 2


ARCH 631

Force Components

Fy

Fx

F

x

y

Fy

Fx

F

Fy

Fx

F

F2018abn

• weight (F = ma)

• concentrated

• distributed

– uniform

– linear

• friction

– F =N

W tA

Analysis 19

Lecture 2


ARCH 631

Load Types

x

0

w

𝑤𝑥

2=𝑊

2

F2018abn

load

w tributary widtharea

• tributary load

– think of water flow

– “concentrates” load of

area into center

Analysis 20

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Load Tracing

width

../animations/unesco_load.mov../animations/unesco_load.mov

F2018abn

• 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

M F d

F

A

C

B

d

Analysis 21

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Moments

F2018abn

• analytically

• free body diagrams

0x xR F 0y yR F 0M M

http://www.physics.umd.edu

Analysis 22

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Equilibrium

F2018abnAnalysis 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

F2018abnAnalysis 24

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Supports and Connections

F2018abnAnalysis 25

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Supports and Connections

F2018abn

x Ax

A

y Ay

A

• “average” x & y of an area

• for a volume of constant thickness

– where is weight/volume– center of gravity = centroid of area

W t A

Analysis 26

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Centroid

F2018abn

2

x cx yI I Ad

• 2nd moment area

–math concept

– area x (distance)2

• need for behavior of

– beams

– columns

Analysis 27

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Moments of Inertia

F2018abnAnalysis 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

F2018abnAnalysis 29

Lecture 2


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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

F2018abnAnalysis 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

F2018abn

Pstress

A

• stress is a term for the intensity of a

force, like a pressure

• internal or applied

• force per unit area

Analysis 31

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Stress

F2018abn

• normal stress is normal

to the cross section

• shear stress parallel

to a surface

t or c

Pf

A

v

P Pf

A td

Analysis 32

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Stress Types

F2018abn

p

P Pf

A td

v

Tf

J

• bearing stress on a

surface by contact in

compression

• torsional stress by shear

from twisting

Analysis 33

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Stress Types

F2018abn

• single shear

• double shear

• bearing

2

4

vd

P Pf

A

2

4

2 2

2v

d

P PP

fA A

p

projected

P Pf

A td

Analysis 34

Lecture 2


ARCH 631

Bolt Stresses

F2018abn

• tension and compressive stress caused

by bending

• shear stress from bending

b

Mc Mf

I S

v ave

VQf

Ib

Analysis 35

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Bending Stresses

F2018abn

longitudinalV VQ

p I

connected area

connector

VQnF p

I

• plates with

– nails

– rivets

– bolts

• splices

Analysis 36

Lecture 2


ARCH 631

Connectors Resisting Shear

x

y

ya 4”

2”

2”

12”

8” p

p p

4.43”

F2018abn

Lstrain

L

Analysis 37

Lecture 2


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Strain

• materials deform

• axially loaded materials change

length

• bending materials deflect

• STRAIN:

– change in length over length

F2018abnAnalysis 38

Lecture 2


ARCH 631

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

F2018abn

• important to us in - diagrams:

– straight section

– LINEAR-ELASTIC

– recovers shape

(no permanent

deformation)

f E

PL

AE

Analysis 39

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ARCH 631

Stress to Strain

f

F2018abnAnalysis 40

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Behavior Types

• brittle

• semi-brittle

F2018abnAnalysis 41

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ARCH 631

Plastic Behavior

• ductile

at yield stress

F2018abn

• if we need to knowwhere max f and fvhappen:

Analysis 42

Lecture 2


ARCH 631

Maximum Stresses

F

1c o s0 oA

Pf max

5.0sincos45

22

maxmax

f

A

Pf

o

v

F2018abn

• - the rate of strain per degree

• UNITS : ,

• length change:

• thermal strain:

– no stress when movement allowed

Analysis 43

Lecture 2


ARCH 631

Thermal Deformation

F C

LTT

TT

F2018abn

• curvature, R

Analysis 44

Lecture 2


ARCH 631

Beam Deflections

EI

M

R

1

EI

xMcurvature

)(

dxEIxM

slope)(

dxEIxM

deflection)(

a l lo wa b lea ctu a lxy )(max

F2018abn

• short columns

• slenderness ratio = Le/r (L/d)

• radius of gyration =

Analysis 45

Lecture 2


ARCH 631

Column Stability

weak axis

aactual

critical FA

Pf

A

Ir

22

2

22

rL

E

LA

EAr

A

Pf

ee

criticalcritical

2

e

2

critical

rL

EAP

F2018abn

• when a column gets stubby, Fy will limit the

load

• real world has loads

with eccentricity

• end conditions

Analysis 46

Lecture 2


ARCH 631

Column Stresses

LKLe

Documents

structural analysis (statics & mechanics)faculty.arch.tamu.edu/.../lectures-631-fall/Files/lect2_ygyIjjK.pdfAnalysis 1 F2018abn Lecture 2 Applied Architectural Structures ARCH 631