introductory mechanics of materials review

8/13/2019 Introductory Mechanics of Materials Review

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3 VKDmge`jngs oh D`tmrn`bs Smvnmw

Mxp`jknjf Mkug`tnoj`b Eornzojs, BBG d`keuv`cbm.orf

(VK.7`)

VK.7 MBMDMJ[@S^ W[S]G[]S@B [EMOSNMW

@ssudptnoj 0< Mxtmrj`b horgms `jk dodmjts `rm jot hujgtnojs oh tndm.

Nh wm rmb`x @ssudptnoj 0, temj tndm dust cm g`rrnmk `s `j njkmpmjkmjt v`rn`cbm, `jk tem kmrnv`tnvms wnte rmspmgt to x

dust cm gojvmrtmk hrod orknj`ry to p`rtn`b kmrnv`tnvm. [em snfjnhng`jt knhhmrmjgm eowmvmr ns nj tem mqunbncrnud mqu`tnojs. Hor tor-

snoj `jk cmjknjf, wm ndposm tem hobbownjf `kkntnoj`b bndnt`tnojs.

Vm bndnt oursmbh to gnrgub`r gross smgtnojs hor torsnoj. [ens pmrdnts us to usm tem `rfudmjts oh `xnsyd-

dmtry nj kmkugnjf kmhord`tnoj.

Hor cmjknjf, wm `ssudm temrm ns ` pb`jm oh syddmtry, `jk tem bo`knjf ns nj tem pb`jm oh syddmtry.

[ens bndnt`tnoj mjsurms syddmtrng cmjknjf. Vm wnbb `ssudm te`t temx-ypb`jm ns tem pb`jm oh syddm-

try `jk te`t cmjknjf ns oggurrnjf `cout temz`xns1 te`t ns, gross smgtnojs rot`tm `cout temz`xns.

VK.7.0 Kmhord`tnoj

Hnfurm VK.3 (`) Gybnjkrng`b prmssurm vmssmb. (c) Wpemrng`b prmssurm vmssmb.

Hnfurm VK.7 Kmhord`tnoj oh strugtur`b dmdcmrs nj (`) `xn`b, (c) cmjknjf, `jk (g) torsnoj dokms. (Gourtmsy Yrohmssor L.C. Bnfoj)

xx

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x

r

y

z

x

(`)(c)

pS

3t-------4 4

Ornfnj`b Frnk

xy

z

Ornfnj`b Frnk Kmhordmk Frnk

(`)

(g)

(c)


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Hnfurm VK.7 seows frnks `s temy kmhord nj rmspojsm to `xn`b, torsnoj`b, `jk cmjknjf bo`ks. [em kmhord`tnoj oh tem frnk ns oj tem sur-

h`gm, cut ko tem ponjts nj tem njtmrnor oh tem gross smgtnoj cme`vm nj ` sndnb`r d`jjmr? @j `hhnrd`tnvm `jswmr to tem qumstnoj ns ` rm`soj-

`cbm `pproxnd`tnoj `s bojf `s tem kndmjsnojs oh tem gross smgtnoj `rm duge sd`bbmr (h`gtor oh 09) te`j tem bmjfte oh tem dmdcmr, wenge

ns ojm oh our bndnt`tnojs. Vm jotm te`t tem hobbownjf ocsmrv`tnojs `rm trum hor `bb termm g`sms. (0) [em mkfms oh tem gross smgtnojs rmd`nj

str`nfet kurnjf kmhord`tnoj, suffmstnjf te`t tem pb`jm smgtnojs rmd`nj pb`jm. (3) [em kndmjsnoj`b ge`jfms nj temyknrmgtnoj `rm jmfbnfn-

cbm (n.m., tem jord`b str`nj nj temyknrmgtnoj ns jmfbnfncbm hor anjmd`tng gojsnkmr`tnojs)1 eowmvmr, tem Yonssoj mhhmgt mjsurms te`t temrm

wnbb cm sodm jord`b str`nj nj temyknrmgtnoj, wenge wm wnbb cm `cbm to hnjk ojgm wm ajow tem jord`b str`nj nj temxknrmgtnoj.

@xn`b


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; VKDmge`jngs oh D`tmrn`bs Smvnmw


ujnhord `xn`b knspb`gmdmjt (u9) smp`r`tmby `s ` procbmd nj `xn`b kmhord`tnoj. [eus, to stuky cmjknjf `jk `xn`b procbmds njkm-

pmjkmjtby, wm wnbb `ssudm u94 9 nj cmjknjf.@ssudptnoj 3g-Cndpbnms te`t tem sem`r str`nj xy ns jm`rby zmro,hor xyns tem dm`surm oh tem ge`jfm oh `jfbm cmtwmmj

tem `xns oh tem cm`d `jk tem pmrpmjkngub`r pb`jm. Vm g`jjot usm tens `ssudptnoj nj cunbknjf temormtng`b dokmbs oh cm`d cmjknjf

nh sem`r ns ndport`jt, `s nt ns nj s`jkwnge cm`ds. Cut @ssudptnoj 3g-Cembps sndpbnhy tem temory cy mbndnj`tnjf tem v`rn`cbm ,wenge rmprmsmjts ` dm`surm oh tem rot`tnoj oh ` gross smgtnoj cy ndposnjf tem gojstr`njt te`t tem `jfbm cmtwmmj `xn`b knrmgtnoj `jk

tem gross smgtnoj ns `bw`ys >9. [ens ns `ggodpbnsemk cy rmb`tnjf to v`s seowj nj Hnfurms K.;g. [em knspb`gmdmjt gurvm ns kmhnjmkcy v(x). [em `jfbm oh tem t`jfmjt to tem gurvm v(x) ns mqu`b to tem rot`tnoj oh tem gross smgtnoj nh @ssudptnoj 3g-C ns v`bnk. Hor sd`bb

str`njs, tem t`jfmjt oh `j `jfbm g`j cm rmpb`gmk cy nts `rfudmjt (n.m., ), wenge wm g`j sucstntutm njto

, jotnjf te`t u94 9 to oct`nj

(VK.8`)

[orsnoj


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=


[orsnoj`)njto

`jk Mqu`tnoj (VK.09`)njto to oct`nj tem hobbownjf strmssms.

VK.7.; Njtmrj b Horgms `jk Dodmjts

Wtrmssms, cmnjf `j njtmrj`b knstrncutmk horgm systmd, g`j cm rmpb`gmk cy st`tng`bby mqunv`bmjt njtmrj`b horgms `jk dodmjts `s seowj nj

Hnfurms K.8`jk Mqu`tnojs (7.;). [emsm njtmrj`b horgms `jk dodmjts `rm `bso rmhmrrmk to `s strmss rmsubt`jts.

@xn`b Cmjknjf [orsnoj

(7.7-@) (7.7-C) (7.7-[)

Hnfurm VK.8 Wt`tng`bby mqunv`bmjt njtmrj`b horgms jk dodmjts.


(7.;`-@)

(7.;c-@)

(7.;g-@)

(7.;`-C)

(7.;c-C)

(7.;g-C)

(7.;-[)

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@xn`b


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tem pob`r `rm` dodmjt oh njmrtn` .

Vm oct`nj tem hobbownjf hordub`s ndpbnms te`tM`jk F`rm gojst`jts cmtwmmjx0 `jkx3.

@ssudptnoj 09, ` seortmr hord oh tem `ssudptnoj fnvmj nj [`cbm 7.7, ndpbnms te`t tem gross-smgtnoj`b kndmjsnojs `rm jot

ge`jfnjf wntex< emjgm@`jkLko jot ge`jfm cmtwmmjx0 `jkx3.Nj Yrocbmds 7.6 teroufe 7.>,@`jkLdust cm houjk `s hujgtnojs

ohx`jk Mqu`tnoj (7.5-@)`jk (7.5-[)njtmfr`tmk to oct`nj tem kmhord`tnoj.

@ssudptnoj 00 ndpbnms te`t njtmrj`b `xn`b horgm `jk tem njtmrj`b torqum `rm jot ge`jfnjf wntex. Nj Yrocbmds 7.7; `jk

7.78 @ssudptnoj 00 ns jot v`bnk, `jk tem njtmrj`b horgm or dodmjt `s ` hujgtnoj ohxdust cm houjk `s kmsgrncmk nj Wmgtnoj

@.03.5, temj Mqu`tnoj (7.5-@)`jk (7.5-[)g`j cm njtmfr`tmk to hnjk tem kmhord`tnoj.

Nh @ssudptnojs > teroufe 00 `rm v`bnk, temj tem hobbownjf hordub`s g`j cm usmk.

VK.7.6 Wnfj Gojvmjtnojs

[em njtmrj`b horgms `jk dodmjts `rm g`bgub`tmk cy d`anjf `j nd`fnj`ry gut teroufe ` strugtur`b dmdcmr, kr`wnjf tem hrmm coky kn`-

fr`d oh ojm oh tem two p`rts prokugmk hrod tem gut, `jk wrntnjf tem mqunbncrnud mqu`tnojs. Cut nj we`t knrmgtnoj seoubk wm kr`w tem

njtmrj`b horgms `jk dodmjts oj tem nd`fnj`ry gut?

Ojm possncnbnty ns to kr`w tem njtmrj`b horgms `jk dodmjts nj ` knrmgtnoj te`t wnbb smrvm to mqunbncr`tm tem otemr horgms. [eus, wm

wnbb `bw`ys oct`nj posntnvm v`bums hor tem njtmrj`b horgms `jk dodmjts. [em strmss `jk kmhord`tnoj hordub`s g`j temj cm usmk

ojby hor kmtmrdnjnjf tem d`fjntukm. [em snfj (knrmgtnoj) oh tem strmssms `jk kmhord`tnoj temj dust cm kmtmrdnjmk cy njspmgtnoj.

[em smgojk possncnbnty ns to kr`w tem njtmrj`b horgms `jk dodmjts `t `j nd`fnj`ry gut `ggorknjf to tem snfj gojvmjtnoj

kmsgrncmk nj Hnfurms K.6. [em mqunbncrnud mqu`tnojs woubk temj fnvm ` posntnvm or jmf`tnvm v`bum hor `jy njtmrj`b qu`jtnty, `jk

tem hordub` woubk fnvm tem gorrmgt snfj hor tem strmssms `jk kmhord`tnoj.

Hnfurms K.6rmprmsmjts tem strmss knstrncutnojs `jk st`tng`bby mqunv`bmjt njtmrj`b horgms `jk dodmjts nj ` fnvmj goorkn-

j`tm systmd. Hrod temsm samtgems, wm gojgbukm te`t oj `j nd`fnj`ry gut surh`gm nj ` hrmm coky kn`fr`d,


(7.5-@) (7.5-C) (7.5-[)

@xn`b rnfnknty 4M@ Cmjknjf rnfnknty 4MNzz [orsnoj`b rnfnknty 4 FL


(7.>-@) (7.>-C) (7.>-[)

@xn`b Cmjknjf [orsnoj`b

(7.09-@)Kmhbmgtnoj oct`njmk cy sobvnjf `

coujk`ry v`bum procbmd. (7.09-[)

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posntnvm njtmrj`b `xn`b horgm Jns seowj `s tmjsnbm,

posntnvm njtmrj`b sem`r horgm Xyns seowj nj tem s`dm knrmgtnoj `s posntnvm xy, posntnvm njtmrj b cmjknjf dodmjtDzns seowj to put tem posntnvmyh`gm nj godprmssnoj,

posntnvm njtmrj`b torqum [ns seowj goujtmrgbogawnsm wnte rmspmgt to tem outw`rk jord`b.

VK.7.5 Mqunbncrnud Mqu`tnojs

Gojsnkmr `j njhnjntmsnd`b strugtur`b mbmdmjt te`t ns grm`tmk cy d`anjf two nd`fnj`ry guts, smp`r`tmk cy ` knst`jgm kx, `s seowj nj Hnf-

urms K.5`jk Mqu`tnojs (7.00), wemrmpx(x) `jkpy(x) `rm tem knstrncutmk horgms nj temx`jkyknrmgtnojs, rmspmgtnvmby, e`vnjf ujnts oh

horgm pmr ujnt bmjfte, `jk t(x) ns tem knstrncutmk torqum, e`vnjf ujnts oh dodmjt pmr ujnt bmjfte.

Hobbownjf `rm tem snfj gojvmjtnojs hor tem knstrncutmk bo`ks

Mqu`tnoj (7.00-@), (7.00`-C), (7.00c-C), `jk (7.00-[)g`j cm njtmfr`tmk to oct`nj tem njtmrj`b horgms `jk dodmjts `s

hujgtnojs ohx. [o oct`nj tem njtmfr`tnoj gojst`jt, tem v`bum oh tem njtmrj`b horgm or dodmjt dust cm ajowj `t sodm ponjt nj tem

njtmrv`b (bmjfte oh tem dmdcmr, usu`bby) oh njtmfr`tnoj, fmjmr`bby tem st`rt or mjk oh tem njtmrv`b.

VK.7.> Knhhmrmjtn`b Mqu`tnojs

Wucstntutnjf Mqu`tnoj (7.5-@), (7.5-C), `jk (7.5-[)njto Mqu`tnoj (7.00-@), (7.00`-C), (7.00c-C), `jk (7.00-[), wm oct`nj tem hobbownjf

knhhmrmjtn`b mqu`tnojs.

@xn`b Cmjknjf [orsnoj`b

(7.03-@) (7.03-C) (7.03-[)xk

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introductory mechanics of materials review

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