Structures 2 Notes

8/19/2019 Structures 2 Notes

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Structures 2

Hibbeler book chapters to do:

Chapter 5 – Torsion

[Chapter 6 – Bending (revision!Chapter " – Transverse Shear

Chapter # – Co$bined %oading

Chapter & – Stress Trans'or$ation

Chapter ) – Strain Trans'or$ation

Chapter * – +nerg, -ethods

%ecture .uestions:

Chapter * (Torsion:

%ook at /ircra't Structures book 'or torsion o' $ulticell thin 0alled sections

1one: .&

3one 4rong:

. – /l0a,s re$e$ber 0hen to round up or to round do0n ,our ans0ers+speciall, in the case o' torsion it is i$portant to so$eti$es round do0n ,our

ans0er – this is 7uite counterintuitive8

.5 – 9 a$ getting an ans0er o' ""

.6 – 4hen dra0ing shear o0 distribution sho0 the arro0s o' the shear o0 too

4hen the 7uestion $entions the ;length< o' a thin section this the longitudinallength % rather than the peri$eter o' the cross section


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=ou al0a,s 'orget to s7uare the area in the calculation o' polar $o$ent o'

inertia

=ou $ade the $istake o' subtracting the shear stresses and 2 to >nd the shear

stress in the $iddle vertical 0eb 9n 'act it 0as necessar, to subtract the shear

o0s and 2 and to then divide the result b, 25$$ to get the shear stress inthe $iddle 0eb

=ou also took the tor7ue value as being ) to the 0hile actuall, it 0as ) ti$es

) to the (ie ) to the * in total

The ans0er 'or the angle o' t0ist given belo0 see$s to be 0rong 9t see$s to be

t0ice the actual value (the person 'orgot the hal' the ans0er at the end

http:??*&"22)*?nptel?CS+?4eb?)5)#)")?$odule"?lecture6pd'

http://14.139.172.204/nptel/CSE/Web/105108070/module7/lecture16.pdfhttp://14.139.172.204/nptel/CSE/Web/105108070/module7/lecture16.pdf


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@rincipal stresses and $aAi$u$ shear stress:

The maximum and minimum normal stress are called principal stresses.The angle ΘP defnes the orientation o the principal planes, that is, the

planes on which the principal stress act.

No shear stress acts on the principal planes.

The planes o maximum shear stress occur at 45 to the principal axes.

The maximum shear stress is one-hal the dierence o the principle

shear stresses.

Hibbeler – -echanics o' -aterials:

@g #" "6 ""

@g *)* ."") (,ou got hal' the original ans0er

The shear centre is the point through 0hich a 'orce can be applied 0hich 0illcause a bea$ to bend and ,et not t0ist The shear centre 0ill al0a,s lie on an

aAis o' s,$$etr, o' the cross section

@g*25

@# ('orces produce bending $o$ent about the centroid no need 'or si$ilar

trinagles or the like


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@g 5& – ,ou 'orgot to put negative signs 'or all ,our ans0ers:

)55 couldn


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Torsion:

ro$ http:??ngu,enhonghai'ree'r?+BDDES?SC9+FC+G2)/F1

G2)+F39F++9F3?-+C/F9.I+?-/T+9/IJ?-echanicsG2)o' G2)-aterialsrarK9%+S?-echanicsG2)o'G2)-aterials?Lolu$e

G2)2?2666K)5pd'

http://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdfhttp://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdfhttp://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdfhttp://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdfhttp://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdfhttp://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdfhttp://nguyen.hong.hai.free.fr/EBOOKS/SCIENCE%20AND%20ENGINEERING/MECANIQUE/MATERIAUX/Mechanics%20of%20Materials.rar_FILES/Mechanics%20of%20Materials/Volume%202/32666_05.pdf


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The shear o0 $easures the 'orce per unit length along the tube


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"i##eler$uestions

%hapter & ' Trans(erse )hear *"i##eler +th edition

1one: " – "5 ." – ."6 (Feed to do revie0 7uestions888

." is a good 7uestion (,ou did this correctl,

."5 is a good 7uestion (0hen integrating 'or area al0a,s put li$its that agree

0ith the positive convention 'or the , and A aAes

."& is a ver, good 7uestion

3ot 4rong:

+Aa$ple " pg 6"

&. =ou needed to 0ork out the >rst $o$ent o' area and thickness o' oneange onl, ( TH9S 9S / L+= 9-@DT/FT CDFC+@T8

"2 This 7uestion got ,ou real bad (=ou should kno0 that the $aAi$u$ shear

stress need not be positive so 0hen ,ou dra0 the shear 'orce diagra$ look at

the point 0ith the highest ;a$plitude< to 0ork out the $aAi$u$ shear stress

"5 =ou $ade a $istake in calculating the second $o$ent o' area

." =ou took the 0rong thickness (,ou took the top thickness 0hich is incorrect

."* (-inor $istake

."6 (or a point belo0 the neutral aAis take the $o$ent o' area belo0 thesection o' the interest

."#

."2 %ook at solution This is ho0 ,ou are supposed to present shear stressdistribution across a crosssection ('ocus particularl, on the e7uation o' the

curve given

." and ."* (=ou calculated the second $o$ent o' area and the >rst

$o$ent o' area incorrectl,


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."5 %ovel, .uestion

."6 =ou got 0recked $ate

%hapter + ' %om#ined /oading *"i##eler +th edition

1one: # – ## ## – #) #6 #" #*# #5" – #5#

#26

3ot 4rong:

#

#2 (e$e$ber that 0hen the point is under the neutral aAis then use . 'or

botto$ section o' the co$ponent

# (=ou calculated the shear 'orce bending $o$ent and . incorrectl,

#* This totall, con'used $e888

#6 Boss .uestion (Fote that the 5))F 'orce induces a shear 'orce torsional$o$ent and bending $o$ent888

#" 4h, 0as the diMerence o' the t0o shear stresses taken and not the su$NNN

##

#2*

#2&

#2

#6

#" (4h, do the shear stresses add upN 9t does not $ake sense


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%hapter 0 ' )tress Transormation *"i##eler +th edition

1one: &&6 &"& .&5 &5# .&"# .&#* – .&&* (Feed to do

revie0 7uestions888

3ot 4rong:

& (orgot to halve angle

&5 (=ou did not $ention the second principal stress ie the algebraicall,s$aller principal stress is e7ual to ) -@a

&6 (9 need to revise bending o' bea$s because the shear 'orce and bending$o$ent that 9 calculated 'or point C 0ere incorrect

+Aa$ple && pg *6" o' book

&) (=ou calculated the nor$al stress 0rong ie $ade a $inor $istake and,ou calculated the shear stress 0rong because ,ou calculated the 0rong value o'

the >rst $o$ent o' area . 0hich 0as supposed to be 'or the top section not thebotto$ one

.&5

.&&2 %ovel, .uestion as it teaches ,ou ho0 to use the sign 'or shear stressesinduced b, shear 'orces (the direction o' the shear stress is the sa$e as that 'or

the point load rather than the shear 'orce


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%hapter 1 ' )train Transormation *"i##eler +th edition

1one: .) – )) (Feed to do revie0 7uestions888 .)22 .)6* –.)# )2 – )5#

5 /F1 5* TD 1D8

)*5 9s a ver, nice concept 7uestion

3ot 4rong: .) )5

.)* (=ou dre0 the angle 'or the last part 0rongO re$e$ber that the positive

value of shear strain $eans that the angle between x 1 and y 1 decreases

.)5

.)2*

.)25

)&

)*)

)* BDSS .I+ST9DF8

)* =ou calculated 9 incorrectl,

)*6

)*# BDSS +.I/T9DF

)*&

)55 %DL+%= .I+ST9DF8 F++1 TD %+/F HD4 TD 1D TH9S888

)56

)5" Ler, nice 7uestion

)5

)5* Beauti'ul8

.)" =ou should $ention so$ething like ;Based on this result the steel shelldoes not 2ield according to the $aAi$u$ shear stress theor,<

.)"5 Ler, nice 7uestion

.)"6

Principal stresses and principal strains

occur in the same directions.

3uctile materials ail in shear and here the $aAi$u$shearstress theor, or

the $aAi$u$distortionenerg, theor, can be used to predict 'ailure Both o'these theories $ake co$parison to the 2ield stress o' a speci$en subPected to


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a uniaAial tensile stress rittle materials ail in tension or compression

and so the $aAi$u$nor$alstress theor, (or -ohr


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%hapter 4 ' nerg2 6ethods *"i##eler +th edition

1one: * – *5 *) ** *&

Fot done: *6 *" *

3ot 4rong: * ** *5


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Structures 2 Notes