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Erbil Polytechnic University Strength of Materials-I (STM303)
Erbil Technical College Dr. Feras Khlef
Civil Engineering Techniques Dept. First Semester 2021
Lecture 17
Bending stress in Beams
Th e b e nding m o m e nt “M” c a uses th e
m a terial within th e b otto m p ortion of th e
b ar to stretc h a nd th e m a terial within th e
to p p ortion to c o m press. C onse qu e ntly,
b etw e e n th ese tw o re gions th ere must b e
a surfa c e, c alle d th e n e utral surfa c e.
Erbil Polytechnic University Strength of Materials-I (STM303)
Erbil Technical College Dr. Feras Khlef
Civil Engineering Techniques Dept. First Semester 2021
Lecture 17
m ax = th e m aximum norm al stress in th e
m e m b er, whic h o c c urs a t a p oint on th e
cross-se ction al are a farth est a w a y fro m
th e n e utral axis.
M = th e result a nt intern al m o m e nt, d etermin e d
fro m th e m etho d of se ctions a nd th e
e qu a tions of e quilibrium, a nd c alc ula te d
a b out th e n e utral axis of th e cross se ction
c = p erp e ndic ular dist a n c e fro m th e n e utral
axis to a p oint farth est a w a y fro m th e
n e utral axis. This is wh ere m ax a cts.
I = m o m e nt of in ertia of th e cross-se ction al
are a a b out th e n e utral axis
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Civil Engineering Techniques Dept. First Semester 2021
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Civil Engineering Techniques Dept. First Semester 2021
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Civil Engineering Techniques Dept. First Semester 2021
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Bending stress in Beams annotated

  • 1. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 Bending stress in Beams Th e b e nding m o m e nt “M” c a uses th e m a terial within th e b otto m p ortion of th e b ar to stretc h a nd th e m a terial within th e to p p ortion to c o m press. C onse qu e ntly, b etw e e n th ese tw o re gions th ere must b e a surfa c e, c alle d th e n e utral surfa c e.
  • 2. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 m ax = th e m aximum norm al stress in th e m e m b er, whic h o c c urs a t a p oint on th e cross-se ction al are a farth est a w a y fro m th e n e utral axis. M = th e result a nt intern al m o m e nt, d etermin e d fro m th e m etho d of se ctions a nd th e e qu a tions of e quilibrium, a nd c alc ula te d a b out th e n e utral axis of th e cross se ction c = p erp e ndic ular dist a n c e fro m th e n e utral axis to a p oint farth est a w a y fro m th e n e utral axis. This is wh ere m ax a cts. I = m o m e nt of in ertia of th e cross-se ction al are a a b out th e n e utral axis !"# $ % & ' ( )* + , -./0-- #1 2 + ###-,34(0(5(3( ) 6 78709. /.:; ;<82. =02./;> ;?:- @ = + A + B <09C:91 D & -291 E & ; #. ; .DF G =01;.:H0 I+ J + K8-:.:H0 I + LM +
  • 3. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 Ex: N87O2.0 P;?:727 <09C:91 QRST -./0-- :9 .U0 <0;7 -U8V9 + " W8> + &XLL . & F YP QPZ -.0O- [ [ ! !/;V I+.. + !:;1/;7 XST S/ & QMST + + 7 ] ^ _8/ `77 + -0>0N. I+ :. + a 7;b _/87 .U0 % 78709. !:;1/;7 [8 J79?%QcS=+[d % e f7;g%P7 h;-0>b "= & A W8>:C /0N.;912>;/ h/8-- & -0N.:89 + i c8N;.0 = + A + ;. .U0 N;7O + QRR77 h/8-- & W0N.:89 f09- j [ #[A N8 k%:-87 & 3 RR77 l , m + e N;>N2>;.0 h[ ;9C hN N87O "h1 :-8 n .U0 ..7/? % &LQMSo + 7 &pL4 + 77 h.N- [09-:89 m &R
  • 4. C& h87O2.0 "9 + A+ _8/ .U0 N/8--&-0N.:89 "9 +;%<" @/0N1.;-912->0;/ + B ?20 % Y88BI 3 -8 LQ = L%M+pMRX B 77 n. qLpR rB #7 + &sa7 .09-:89 a77 + "=A + h j QM`R`B * Lp4 #70? & .8 %Z=L77&f [ "= n A aV; + _ h N87O + t_0"#:M877" & "= + A +
  • 5. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 Ex: h0;-0 Q ) I8? N/8--&-0N.:89 h89-:C0/ .U0 W;70 <0;7 QRR77 V:.U .U0 W;70 c8;C:91 P890b + &MMQMS4 G -8 "S877 " 77 & c8N;.0 H+ A + fap8 h87O + _:<0/ "u879 & VVV+:-.8-:.:H0&-:___ j :. :. h [_ QRU7 Q8U7 & "= +A + [09-:89 _:<0/ % '8/ .U:- <8? N/8-- & W0N + 2-0 K;/;>>0> ;?:- .U08/07 "= + A + @ "O;/.. AO;/. + CQ B " +(#.vAiC!j. " w^.A^Cuxv C+ _. & y & ".n- + Q e i = & w . z j C:__ [CM%8A w ; z k ^ [8 M
  • 6. QRR & C+ _. & y & 4 + (4 + #>: )( + "^ & "-8 " "9 + A + %""" f88 * QRgLpR&QppL*Q v wQRrMQ`rY&v`*Q`RY`LQz A Q&&QLp`pYYYY U:7 M E/09 + + $ &LMS4 6 + a"[ { % Y& $ ## LQ%QLp`pYYYY 77 n. `7"g%P79 QML4pM _.O+"[O;_ "= + A % QLp`pYYYY _99S&:.71+9+NNd+&Y||)n-"YC>`":;x
  • 7. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 Ex: h;-0 Y { " & W0N.:89 u8877 W;70 <0;7 ;9C c8;C:91 -8 77 & y & h89C:.:89 &RLM77 3 "-87 & a_; kQMS= & 7 /&u88+7bd##A A= & A + :9 .U0 7:CC>0 ;7 & Wb7 j u879 ^ LLpR77 h[ "N0 &MpR77 }Q887d "9 + 9;.:89 )! +-: " A C w LQRYjQQ&`RYYv@QR*Q`~`pB%LX`Y`RR`R 77M #9; n"%#:g(C<IaK" m N87O/0--:89 _:<0/ LpRZ " m & LpR%QL " v .09-:870.0/
  • 8. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 Ex: a:7 jttM"0N.:7D3?V8• W0N.:89 :- 98. 1b7 + €887 " c8N;.0 = + A + % ". €8/9 & A9 + ; j &L Au;u "- 4Q ; j ;/0 3 % @QRRtQRrMR~Bv@QRtRYLQLRB '8V0b & -8 d @ Qt~QRrvpQR •u88 B j [ 3hN G :-&77;+-2d8_*8&:"":"‚:; 6 n l N % QQR&Lpp%`p 77 < } < * h[ % Lpp77 €8/9 & h j "99 + _.O+/.:&AO;/.&Cb..7;?::-1505:.+:9k+O87-0/ [09-:89 _:<0/
  • 9. Erbil Polytechnic University Strength of Materials-I (STM303) Erbil Technical College Dr. Feras Khlef Civil Engineering Techniques Dept. First Semester 2021 Lecture 17 Ex: V891 f## i [a" ) = d & & A + :- +"[d:8&""88+088 v ": "[P & Y A. C j "= +11k_pk.u88B&&cu8;28B@>pp&>88'x. f88-0 B@ `p & >8. z %Y &r`````r77 n. ( h87O/0--:89 _:<0/ hN h89_O:/U0-0-1:89 hEPK[ q h;-. f/00S % &QMM4 B N qs + & Yr`````r A + [09-:89 {[:; N j 4LppL ƒ ƒ & & q [09-:89 _u11.09-: QMMR`ƒ@Lp&pB _:<0/ Yr`````r&&LpX+XLMLYr