In-depth lecture notes for MIT's 2.001 Mechanics and Materials I course covering statics, bending, torsion, and more. Examples and problem solving strategies are covered in the notes.
2 001 Mechanics and Materials Lecture Notes
Lecture 1 Axial Loading and Free Body Diagrams
Objective Preventstructural failure inability toperformfunction by controlling
deformatio
controlling
E
deformation
Structural Elements In 2.001
4 Bars in axial loading 4 Thin wall pressurevessel
soda can opening
F OF
2 Shafts in torsion 5
Buckling ofcolumns
of y
3 Beams in
bending
Fdionfonat.tt force tongueequilibrium loading reactions latstructure
internalresultants atsections
stress atpoint
I dieffinghoents Petitions lat
structure
2 Geometric
compatibility
strain atpoint
itsmaterial constitutiveresponse materialbehavior
elastic
stress a strain latpoint
elastic
Start in ID straight bar in axial loading plastic
force in ID É Ey
any
8
Éx o Ie p x
I
qq.gg
FA FB Forces vector
In 2.001 knownforces in sketches draw arrow directionofforce
in
indicate magnitude on arrow
ex
I W Wxt
of go
p Px X We O R E
E Fa dingytiongnaccounted
GivenFA F bar in equilibrium
static equilibrium in ID zero accelerationeverywhere
gp o sum offorces
tryingto acceleratestructuredirectio
in x
Fx 0 F B FA 0 FA FB F condition for F F
equilibrium
convention
sign
I gig F Qa Fx O F F O
, Reaction at supports
I
TheWall
Bse s wall preventsdisplacement
providingreaction unknownR'along'x
RI RI I
To find unknown outwhereunknownacts
starting at the art draw isolationbubble aroundbodywewan.it
redraw everything insidebubble unknown atont e
imposestaticequilibrium on FBD find unknown
FreeBodyDiagrams FBDs
Draw FBDoteverythinginsidebubble
1 Remove wall
Iga By
2 Replacewall w unknownreaction
on In2.001 we drawunknownforcesthe wouldact it
waythey
positive
Rig ye I 3 Imposeequilibrium
Fx O RI F O RE F RE GFI
ifobtain unknown
Fy HF Fx F F O directionof arrow insolved
Epp flipdirection
Forbanet Fx F F O structure as a whole is in equilibrium but
wantequilibriuminsidetheband aswell zero acceleration
N Internal NormalForce Resultant everywhere
F
It signconvention N
axial
Tension 0 t
5 If itunknown draw Oltofontsection
Given F howdo we obtain N
A After out isolationbubble
e pickbubble drawF'Bb
Imposeequilibrium FBDI EF O N F NEF
BUBBLE I BUBBLE2 FBD 2 IF O F N Nc F
General C unknown find me garters
equilibriu
f is i I
ebb Iggy FBD2 g c n
plotNext the axial force
diagram
3rd Law Na Note tensile N is got to
ION N ION
My compressive N is 0ft
snappy
x
gg
MMM
SN
Vote We can drawbubbles w 2 ants to relateresultants at differentsections
TF se i w p s
setidection Ex D W Pt N
N
Ma N W p
, Geometric
A
compatibility
B
indeformed
1g L Loss elongation structural
signconvention 8800 bar
to of
elongates irrespective
axis
bar shortens x
deformed 1 8 Totalchange inbarlength
Note I 2
3
L
8 81 82 8
g g g
Elasticstiffnessof bar in axialloading
Linking San
homogeneous linearelasticmaterial
AN
Ma cross section uniform cross section
area uniform resultant N
virtual experiment
Hy dog n applyn measures
stiffness
K
Y structural
property
8 S
E Young's
Sa Na Pa modulus
Geometric dependence of k needto normalize Hooke's Law
3 steel Bars
o Ee
A diamond TENSION
a
bar 2 2A Ly
steel or
bar Ault m lite
yegg maybe ekunload
bar A 24 Er
Sho e
Equilibrium Esma
141A O
signconvention at
o ngam
Mma Pa
o tensile
1 O K
Compatibility ocompressiv
I 18 axial strain E
signconvention extensio
I E mm L compressio
Uniform same along x homogeneous I material bar
S Lot
I bar segment constant
A length Lo
strain E
uniformelongationper length
AreaA
uniform force per unit area
to A stress o N A Pa
L
N OA EEA SEA
da 0ft bar stiffness
, Lecture 2
General caseotelasticbarinaxialloading
1 Displacement
compatibility
I displacementrector
materialpoint Pax
jefmfedmYa u x componentof it
FE.T.io uisafield it changes w position
za 7
pointmoresalonyx air ask
Ux p iY
ex W XP
212.001 Kinematic Assumption In Axial Loading y 2t
All points on section samexplharethesameux
P
crosssection mill remain
flat normal tox NOTE this is valid forsmoothly
cross sections
Ux Oat wall ux xp o varying
Ej u
oalongi
o
I
u against'x
3 Deformation strain Field
to
nngIteihind'uixtaxi.ua strain elongation
gigittl
ftp.qq
E x day
initial length
eweulxtdgt ulxl.dk
NOTE We can have E Oatwall
displacement up
gradient
One hpeto
4 Strain Field Displacement Field
EW day if we know eat reintegratetogetulx
but we needboundaryconditions Bcs
If I know ulxo no
ulxi ulx.lt ddylx'ldx
UCH not ÉE x dx
NOTE n Oat wall free BC
UH O O
I E x 0.0240.01
I I L
E
UN MIO Sto 01 0.021 dx
2
MMM 0.01 0.01 L
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller jasonchen2025. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
