Analysis ntawm beams nyob rau deflection. Qhov siab tshaj plaws deflection ntawm lub beam: lub mis

Nqaj - caij engineering ntawm ib tug pas nrig uas yog loaded nrog rog kuj nyob rau hauv ib tug coj lawv mus rau lub pas. Kev ua ub no engineers feem ntau yuav qhov yuav tsum tau los mus laij lub beam deflection nyob rau hauv load. Daim ntawv no yog ua nyob rau hauv thiaj li yuav txo tau lub siab tshaj plaws deflection ntawm lub beam.

hom

Rau hnub tim, cov kev siv yuav tsum siv beams ua los ntawm ntaub ntawv sib txawv. Qhov no yuav ua tau ib tug hlau los yog ntoo. Txhua cov ntaub ntawv implies ib tug txawv beam. Lub xam ntawm beams nyob rau deflection yuav muaj tej yam sib txawv uas tshwm sim nyob rau hauv lub hauv paus sib txawv nyob rau hauv cov qauv thiab cov cov ntaub ntawv siv.

ntoo kab teeb

Niaj hnub no tus neeg siv implies ib tug thoob plaws siv beams ua los ntawm cov ntoo. Yuav luag txhua txhua lub tsev muaj ntoo plag tsev. Cov kab teeb ntawm ntoo yuav siv tau raws li cov kabmob hais, lawv yog siv thaum lub sij hawm siv thiab ua cov plag tsev, raws li zoo li txhawb rau slabs ntawm plag tsev.

Nws yog tsis muaj daim card uas ntoo, raws li tau zoo raws li steel beam, nyhav sag nyob rau hauv tus ntawm kev nyuaj siab rog. Xub deflection yog nyob ntawm seb cov ntaub ntawv uas yog siv, cov geometric tsim yam ntxwv, nyob rau hauv uas ib tug beam yog siv, thiab qhov xwm ntawm loads.

Cov pub deflection ntawm lub beam yog tsim los ntawm ob yam tseem ceeb:

• Ua raws li deflection thiab permissible qhov tseem ceeb.
• Tseem ntawm kev siv ntawm lub tsev, noj mus rau hauv tus account lub deflection.

Ua thaum lub sij hawm qhov kev siv ntawm lub dag lub zog thiab rigidity cia qhov zoo tshaj plaws kev txaus siab rau dab tsi lub load yuav withstand lub tsev thaum lub sij hawm lub lag luam. Tsis tas li ntawd, cov suav cia rau paub raws nraim li cas yuav ua tau tus yam ntxwv hais deformation nyob rau hauv txhua rooj plaub. Tej zaum tsis tau muaj ib tug yuav cam nrog tus tseeb hais tias lub feem ntau ncauj lus kom ntxaws thiab meej laij - nws yog ib feem ntawm txoj hauj lwm ntawm pej xeem engineers, tab sis tag nrho cov tseem ceeb tsim nyog yuav tau payment siv ib tug xov tooj ntawm cov qauv thiab zauv kev txawj ntawm nws tus kheej.

Nyob rau hauv thiaj li yuav ua ib tug muaj tseeb muab xam los ntawm beam deflection, ib tug yuav tsum tau siv sij hawm mus rau hauv tus account lub fact tias cov kev tsim kho ntawm lub tswvyim ntawm rigidity thiab lub dag lub zog yog inseparable. Raws li cov ntaub ntawv los ntawm lub xam ntawm lub dag lub zog, koj yuav tau npaj mus rau ntxiv xam cov txheeb ze nruj. Nws yuav tsum tau muab sau tseg tias muab xam los ntawm beam deflection - ib qho ntawm lub ntsiab tseem ceeb ntawm lub xam ntawm tus nruj.

Xyuam xim rau lub fact tias rau cov suav koj tus kheej yog zoo dua siv aggregated suav, resorting mus rau ib tug es yam yooj yim tswvyim. Nws kuj pom zoo ib tug me me paj tau paj nyob rau hauv ib txoj kev loj. Tshwj xeeb tshaj yog yog hais tias tus xam kev txhawj xeeb cab kuj hais.

Analysis ntawm beams nyob rau deflection. lub algorithm

Nyob rau hauv qhov tseeb, lub algorithm los ntawm cov uas ua ib tug zoo li muab xam yog heev yooj yim. Raws li ib qho piv txwv, xav txog ib co yooj yim zog daim duab ntawm xam, yog li twg tej lus thiab cov qauv. Nyob rau hauv kev txiav txim los mus laij lub deflection ntawm tus kab teeb rau, ua cov nram qab no cov kauj ruam nyob rau hauv kev txiav txim. Lub algorithm ntawm lub xam ntawm cov hauv qab no:

• Muab xam los tswvyim no yog ua los.
• Txiav txim geometrical yam ntxwv ntawm lub beam.
• Xam cov nyiaj pab ntau tshaj load rau lub caij.
• Nyob rau hauv cov ntaub ntawv ntawm kev xav tau raug qhia tau tseeb ntoo zog rau dabtsi yog khoov caij.
• Computes lub siab tshaj plaws deflection.

Raws li koj tau saib, tag nrho cov kauj ruam yog haum yooj yooj yim thiab yog ua tau.

Kev npaj muab xam tswvyim beams

Nyob rau hauv thiaj li yuav ua lub xam tswvyim, nws tsis yuav tsum tau ntau npaum li cas paub. Nws yog txaus rau paub qhov luaj li cas thiab zoo ntawm tus ntoo khaub lig seem ntawm lub caij, lub luv ntawm txoj kev txhawb zog thiab cov qauv ntawm cov kabmob. Span yog qhov kev ncua deb ntawm ob cov kev txhawb zog. Piv txwv li, koj siv cov beam raws li lub txhawb tuav tshooj rau kev coj tus kheej cov phab ntsa ntawm lub tsev, cov uas 4 m, lub luv nqi yuav ua ncaj rau 4 m.

Xam lub deflection ntawm ib tug ntoo beam, lawv suav tsuas txhawb cov ntsiab ntawm cov qauv siv. Nyob rau hauv cov ntaub ntawv ntawm pem teb beams rau lub xam yog coj los ntawm cov Circuit Court load yog faib tusyees. Nws denoted lub cim q. Yog hais tias lub load yog muaj lub nyob rau hauv cov xwm, uas yog coj los ntawm cov concentrated load Circuit Court, denoted F. Cov magnitude ntawm no load yog sib npaug zos rau tus luj, uas yuav tso siab rau tus qauv.

lub caij ntawm inertia

Geometric yam ntxwv, hu ua lub caij ntawm inertia, yog ib qho tseem ceeb nyob rau hauv cov lus teb rau cov deflection ntawm lub beam. Cov mis tso cai rau koj los mus laij cov nqi no, peb muab nws ib tug me ntsis tsawg dua.

Thaum xam lub caij ntawm inertia yog tsim nyog them sai sai rau lub fact tias qhov luaj li cas ntawm qhov no feature nyob rau dab tsi lub orientation ntawm lub caij nyob rau hauv qhov chaw. Yog li muaj ib tug rov qab sib raug zoo ntawm cov inertia sij hawm ntawd thiab deflection kom muaj nuj nqis. Tus me dua cov nqi ntawm lub sij hawm ntawm inertia, ntau dua qhov lub deflection nqi thiab vice versa. Qhov no dependence yog heev yooj yim mus taug qab nyob rau hauv xyaum. Txhua tus neeg yeej paub hais tias lub rooj tsavxwm, pw rau ntug, flexes ntau tshaj ib tug zoo li board, uas yog nyob rau hauv lub qub txoj hauj lwm.

Suav lub caij ntawm inertia rau ib tug nqaj nrog lub ntoo khaub lig seem los ntawm cov mis:

J = b * h ^ 3/12 qhov twg:

b - sectional dav;

h - qhov siab ntawm lub beam seem.

Xam cov nyiaj pab ntau tshaj load theem

Txiav txim lub siab tshaj plaws load rau hauv structural neeg ua noj mus rau hauv tus account ib tug xov tooj ntawm lwm yam thiab metrics. Feem ntau yog thaum xam xyuas cov load theem noj mus rau hauv tus account tus luj ntawm 1 'meter' beams, tus luj ntawm 1 square meter qab nthab, ru tsev load thiab lub ib ntus xwm ntawm lub load los ntawm cov phab ntsa rau lub 1 square meter qab nthab. Tsis tas li ntawd yuav siv sij hawm mus rau hauv tus account qhov kev ncua deb ntawm lub beams yog ntsuas nyob rau hauv meters. Piv txwv li, xam cov nyiaj pab ntau tshaj load rau ib tug ntoo beam coj nruab nrab qhov tseem ceeb, raws li uas tus overlap luj yog 60 kg / m², ib ntus ru tsev load yog 250 kg / m², partitions yuav luj 75 kg / m². Tus luj ntawm lub beam yog heev yooj yim mus xam, paub nws lub ntim thiab ceev. Xav hais tias uas siv ntoo beam seem 0,15h0,2 m. Nyob rau hauv cov ntaub ntawv no, nws hnyav yuav tsum muaj 18 kg / khiav 'meter'. Tsis tas li ntawd piv txwv li, xav tias qhov kev ncua deb ntawm lub kab teeb sib tshooj ntawm 600 hli. Nyob rau hauv cov ntaub ntawv no yuav tsum tau piv 0.6 peb.

Raws li ib tug tshwm sim ntawm kev xam lub siab tshaj plaws load peb muab tau cov nram qab no tshwm sim: q = (60 + 250 + 75) * 0.6 + 18 = 249 kg / m.

Thaum cov nqi tau, nws puas yuav tau tsiv mus nyob rau lub xam ntawm ntau deflection.

Xam tus nqi ntawm cov nyiaj pab ntau tshaj deflection

Thaum peb xam lub beam, cov mis qhia tag nrho cov tsim nyog hais. Nws yuav tsum tau borne nyob rau hauv lub siab hais tias cov mis siv rau lub xam, tej zaum yuav muaj ib tug me ntsis txawv saib, yog hais tias tus xam yog nqa tawm rau ntau hom kev loads, uas yuav muaj kev cuam tshuam rau lub beam.

Ua ntej peb muab koj lub mis uas siv los laij cov nyiaj pab ntau tshaj deflection ntoo kab teeb nrog rau ib tug faib load.

f = -5 * q * l ^ 4/384 * E * J.

Nco ntsoov tias nyob rau hauv cov mis no, E - yog ib tug tas mus li, hu ua tus elastic modulus ntawm cov khoom. Rau cov ntoo, qhov no daim duab yog 100 000 kg / m².

Ntxiv nrog peb xam cov ntaub ntawv siv rau Piv txwv li, peb tau hais tias, rau kab teeb ntawm ntoo, uas nws tus ntoo khaub lig seem yog 0,15h0,2 m thiab qhov ntev yog 4 m, tus nqi ntawm cov nyiaj pab ntau tshaj deflection thaum raug rau ib tug faib load yog sib npaug zos rau 0,83 cm.

Thov nco ntsoov tias thaum ua deflection xam noj mus rau hauv tus account lub Circuit Court nrog ib tug concentrated load, cov mis yuav siv sij hawm nram qab no daim ntawv:

f = -f * l ^ 3/48 * E * J, qhov twg:

F - tus quab yuam ntawm siab nyob rau hauv lub cav ntoo.

Tsis tas li ntawd mloog mus rau qhov tseeb hais tias tus nqi ntawm cov modulus ntawm elasticity siv nyob rau hauv cov lus teb yuav txawv rau ntau hom ntoo. Pawg tsis tau tsuas yog lub hom ntoo, tab sis kuj lub hom ntawm ntoo. Yog li ntawd, tag nrho cov beam ntawm ntoo, laminated veneer lumber thiab hloov cav yuav muaj txawv moduli ntawm elasticity, thiab chaw pib sib txawv tseem ceeb ntawm nyiaj pab ntau tshaj deflection.

Koj muaj peev xwm caum txawv cov hom phiaj, ua rau lub xam ntawm tus kab teeb nyob rau hauv lub deflection. Yog hais tias koj xav paub txog cov kev txwv ntawm deformation ntawm cov yam ntxwv hais, ces qhov kawg ntawm lub xam ntawm lub deflection ntawm lub xub, koj yuav nres. Yog hais tias koj lub hom phiaj - mus tsim kom muaj lub theem ntawm kev ua raws cai pom kev ntsuas ntawm lub tsev lis dej num, lawv yuav tsum tau muab piv nrog rau cov ntaub ntawv, uas yog muab tso rau hauv tshwj xeeb cov ntaub ntawv ntawm ib tug normative xwm.

I-beam

Thov nco ntsoov tias qhov kuv-beam girders yog siv tsawg zaus vim hais tias ntawm lawv cov lawm. Tab sis kuj tsis nco qab hais tias xws li ib tug tsim lub caij yuav mas ntau dua load dua lub cheeb tsam los yog channel, uas yuav ua tau ib tug lwm txoj rau I-beam.

Muab xam los ntawm deflection H-beam sawv mus ua nyob rau hauv cov kev tshwm sim hais tias koj yeej yuav tau siv nws li ib tug haib tsim lub caij.

Thov tseem nco ntsoov hais tias tsis yog tag nrho cov hom ntawm tus I-beam girders yuav xam deflection. Nyob rau hauv tej rooj plaub, txawm li cas los, tso cai los mus laij lub deflection H-beam? Nyob rau hauv tag nrho xws li tus neeg mob 6, uas sib tau rau hom I-kab teeb. Cov hom yog raws li nram no:

• Ntaus ib leeg-ncua beam nrog ib tug uniformly faib load.
• Console Txhav kos nyob ib ncig thiab uniformly faib load.
• Lub beam los ntawm ib tug ntsua kev mus rau lub console nrog ib tug txhais tes, uas yog thov kom muaj ib uniformly faib load.
• Tib beam nrog ib tug pob khawm hom kev coj tus kheej nrog ib tug concentrated quab yuam.
• Ib leeg-ncua tsuas txhawb beam nrog ob tug concentrated rog.
• Console nrog ib tug txhav kaw thiab concentrated quab yuam.

hlau beams

Lub xam ntawm lub siab tshaj plaws deflection ntawm tib yam, seb nws yog ib tug steel beam los yog ib tug keeb ntawm ib tug txawv cov ntaub ntawv uas. Qhov loj tshaj plaws - nco ntsoov cov neeg tseem ceeb uas yog hais thiab ruaj khov, zoo li piv txwv li modulus ntawm elasticity. Thaum ua hauj lwm nrog hlau beams, nws yog ib qho tseem ceeb yuav tau nco ntsoov hais tias lawv muaj peev xwm yuav ua los ntawm steel los yog ntawm ib qho kev I-beam. Deflection hlau beam ua los ntawm steel, yog xam xav hais tias lub qhov E nyob rau hauv cov ntaub ntawv no yog 2 × 105Mpa. Tag nrho lwm yam hais, xws li lub sij hawm ntawm inertia, yog xam raws li lub algorithms piav saum toj no.

Lub xam ntawm lub siab tshaj plaws deflection ntawm ib tug nqaj nrog ob tug txhawb

Raws li ib qho piv txwv, xav txog ib tug tswvyim nyob rau hauv uas lub beam yog nyob rau hauv ob txoj kev txhawb zog, thiab thereto yog thov concentrated quab yuam nyob rau ntawm ib arbitrary point. Kom txog rau thaum lub caij uas tso npe thov ib tug quab yuam beam yog ib tug ncaj kab, tab sis nyob rau hauv tus ntawm rog tau hloov nws cov tsos thiab vim hais tias ntawm lub lim los ua nkhaus.

Piv txwv hais tias lub dav hlau XY yog lub dav hlau ntawm symmetry ntawm lub beam nyob rau hauv ob txoj kev txhawb zog. Tag nrho cov loads sawv hauv lub beam nyob rau hauv no lub dav hlau. Nyob rau hauv cov ntaub ntawv no, qhov tseeb yog hais tias tus nkhaus tau raws li ib tug tshwm sim ntawm lub dag zog yuam, kuj yuav nyob rau hauv no lub dav hlau. Qhov no nkhaus yog hu ua tus elastic kab ntawm ib beam los yog kab beam deflection. Algebraically daws ib qho elastic kab ntawm ib beam thiab xam lub deflection ntawm lub beam, cov mis uas yog tsau mus rau lub beams nrog ob pab, raws li nram no.

Cov deflection ntawm ib tug deb z los ntawm sab laug nyiaj yug beams rau 0 ≤ z ≤ ib tug

F (z) = (P * ib tug ² * b ²⁾ / ^(6E * J * l ) * ( 2 * z / a + z / bz ^3/2 * b)

Deflection ntawm lub beam nyob rau hauv ob txoj kev txhawb zog ntawm ib tug deb z los ntawm sab laug them nyiaj yug rau ib tug ≤ z ≤l

f (z) = (- P * ib tug ² * b ²⁾ / (6E * J * l ) * ( 2 * (lz) / b + ( lz) / A- (lz) ³ / a + b ^2), qhov chaw uas F - thov dag zog yuam, E - elastic modulus ntawm cov khoom, J - axial lub caij ntawm inertia.

Nyob rau hauv cov ntaub ntawv ntawm ib tug nqaj nrog ob tug txhawb lub caij ntawm inertia yog xam raws li nram no:

J = b ₁ h ₁ ^3/12 qhov twg b ₁ thiab h ₁ - lub dav thiab qhov siab ntawm tus ntoo khaub lig seem ntawm lub beam siv, ntsig txog.

xaus

Nyob rau hauv xaus, nws yuav tsum xaus lus tias samstoyatelno xam cov nyiaj pab ntau tshaj deflection ntawm lub beam ntawm ntau hom yog heev yooj yim. Raws li muaj nyob rau hauv no tsab xov xwm, cov tseem ceeb tshaj plaws - mus paub ib co ntawm cov yam ntxwv uas yog nyob rau hauv cov ntaub ntawv thiab duab yam ntxwv, thiab ua suav rau ob peb cov qauv nyob rau hauv uas txhua parameter muaj nws piav thiab yog tsis coj tawm ntawm tsis pom qhov twg.