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Unformatted text preview: [:JDEJCJ ENGINEERING 2P04  Topic: 4 Member E nd Reactions Member Internal Ferees
Shear Feree 8.: Bending Mement Diagrams
Feree 8.: Relatiens Between Leads, Shear Bending Mements Summary: Preeedures fer Analysis at Shear Farce 8.: Bending Mement Diagrams MEMBER END REACTIONS Member end reeetiene Member end reactions are ueueliy given eleng the glebel eeerdinete directiene. See eeureewere figure MEMBER INTERNAL FORCES Internal Ferees Gleeelly: H5 = Ezﬁtﬂ = it Take a cut and replace eee efthe members {1] with en equivalentferee end eeuele system and eteee 'D' etthe eut: Ifwe IeeIc etthe ether memleerIIEL the internal ferees and eeuete will be equal and eeeesite: Internal ferees ere nermetly expressed in terms eta nermel eempenent and ﬂ SHEET" tempenent: Te maintain a righthand rulei we must eensider the positive sense ef'rnternel ferees {see eeursewere figure]. Stress Hesultants in Beams {SHEAR FDHCE El. BENDlNG MOMENT
DIAGRAMS] Censider a statically determinatei simply supported beam 1with a distributed lead and a paint lead: Cut the beam at pesitien 'x': i] a distributien ef cantaetferees aets an the exposed surface at '3'
ii] eentaet ferees are called stress vecters when they act ever unit elements at the eressseetien iii) stress veeters are statit:al1._I indeterminate
iv} stress veeters can be replaced by an equivalent farce system at the eentreid Ccnsicler a planar state cfstress: subscript '3' means acting cn cut face with urtt ncrmai in xclirecticn. 3: acts en a crcsssecticnal eiement dFi Iccatecl by pcsiticin vectcr 'r’: rel ative tn the centrciicl. The ncrrnai stress CDFHDDHEFIL an 1 acts perpendiculartcthe crcisssecticin. The shear stress ccmpcnenti U331 acts tangential tc the crcsssecticn. Fcrexternaily staticaliy cleterminate beams, the equivalent fcrce system cfthe stresses ccnsists fc a stress resuttant. FIE: ﬂ)ancl stress ceuple; ﬂ) where Iii[71(3) = ﬂIdA ie the differential etreeeferee acting ever CIA. Referring F103) tn the base frame efreferenee gives: F40) 'rs the nermef stress resultmL er 'N.‘ F110) Is the transverse shear stress resultant1 er 'V.‘ The stress eeuple: fer a symmetrfeet eressseetien end planer state of stress: Mz( a) is called the bending mement about the zexis. i) Nermel feree diagram: ptet N vs. 1: H] Nerrnet feree diagram: plet kiss. it Iii} Nerrnel feree diagram: plet M2 vs. 1: Euier'e Field Eguatibne A beam with generai distributed lead. Seetibn the beam at 'xi' ebbwing end reeuitante. Cbneidertbe F.B.D. bf the email beam element 'ﬂx.‘ Equilibrium at x + :53: Dividing by Ed: and taking the limit it: * I}: i) usually P: = [I
ii] fur a unifdrmlv distributed ldad1 the shape dfthe shear curve is negative and
the value at the stage is equal tn the lead per unit length iii] the stage bfthe bending mament curve is equal tn the value at the shear. tfwe integrate equetten 2] between twe peinte. C E. D. en a beam: lfwe integrate equetten 3] between C 3. D: Exemgle '~" [XII “(in r" —‘~.____ EXAJ[PLE : 4—4 For the beam loaded as 511011.711 in the ﬁgure. express the shear force and hendmg
moment by algebraic expressions for the interval AB shown, and then plot the
shear force and bending moment diagrams. Earn' E‘no 3%., EXAJ[PLE : 4—5 Plot the Shea: force and bending 1nmnent diagrmni fur the beam AB 51101111 main EXAJ[PLE : 4—15 The Figure shows a beam AF subjected to distributed loads. Note that the beam segment ABCD is roller supported at B. pinsupported at C. and pinconnected to beam segment D1: at D. The beam segment DP is pinconnec ted to beam segment ABCD at D, and is roller supported at E. (a) Determine the support reactions at supports B. C, and E. {b} Draw to scale. the shear and bending moment diagrams for the beams AD
and DP [Clear explanations and background information related to
construction of these diagrams are expected] (c) Detenuine the location and magnitude of the largest shear force (:1) Detenuine the location and magnitude of the largest bending moment 5 th'
aokHan / mm P'" 4t) thn 4U RN! :1
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This note was uploaded on 02/19/2010 for the course ENG 2P04 taught by Professor Sivakumaran during the Spring '10 term at McMaster University.
 Spring '10
 Sivakumaran
 Statics

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