design to minimize deflection

8/9/2019 Design to Minimize Deflection

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Design To Minimize Deflection

by John F Mann, PE source : http://www.structural101.com/Beam-Design---Basic.html

Structural elements must be esigne to satisf! re"uirements for strength# topre$ent failure or collapse# an stiffness# to pre$ent e%cessi$e mo$ement or

eflection. This iscussion is focuse primaril! on eflection of beam elements. Design of man! beam elements# such as floor &oists# is often go$erne b!

eflection# not strength. This means that# for the re"uire or proposeconfiguration# the limit for eflection is reache before the limit for strength. Determination of the appropriate limit for eflection is one of the first issuesthat must be a resse uring the esign process. See '(oo )raming )or Tile)looring' for a itional iscussion of eflection limits. *f course# there is usuall! a tra e-off between more conser$ati$e esign ancost. +reater strength an stiffness generall! costs more. ,owe$er# there areoften wa!s to impro$e a esign that can actuall! minimize eflection whilere ucing cost. *b$iousl!# a conser$ati$e eflection limit can be specifie to minimize

eflection# assuming esign an construction is then performe correctl!. ,owe$er# it is more useful to fin wa!s to minimize eflection b! moreefficient esign. Basic Metho s )or a gi$en esign loa # the following wa!s if feasible are most often use tominimize eflection# in general or er of ma%imum effect or practicalit!

1 Decrease length of beam Mo$e one or both supports inwar from en of beam 2se moment &oints at en s of beam

3 4ncrease beam moment of inertia5 4ncrease beam mo ulus of elasticit!6 Decrease loa on beam7 Share loa with other beams8 9restressing camber
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Deflection is highl! epen ent on length of beam element. )or a gi$en totalloa an istribution# eflection $aries with the cube thir power of spanlength. Therefore# if length of beam is ouble # eflection increases b! afactor of 8# which is cube ; .

ot onl! is ma%imum span length re uce # but loa on thecantile$er actuall! causes upwar eflection in the main spanthat offsets eflection ue to loa on the main span. ,owe$er# a loa case

without li$e loa on the cantile$er shoul alwa!s be consi ere . See below forfurther iscussion of this metho for a line of multiple beams. Deflection is re uce when one or both en s of a beam resist moment# insteaof being completel! free to rotate 'hinge ' . This metho is generall!a$ailable for steel or reinforce concrete construction# not woo .

Deflection is irectl! proportional to beam moment of inertia# mo ulus ofelasticit! an # for a gi$en loa istribution# total loa . )or the same amount of material# some shapes such as 4-beam ha$e

greater moment of inertia. ,owe$er# increasing epth of a beam is the mostpractical wa! to increase moment of inertia.

Mo ulus of steel is essentiall! the same ?#000 psi for all the $arious gra esan allo!s.

Mo ulus of woo $aries significantl! between species an gra e. Mo ulus canbe increase substantiall! b! using =@= laminate $eneer lumber .

Mo ulus of concrete $aries with compressi$e strength# but is not especiall!sensiti$e.

Stan ar co e pro$isions inclu e generous safet! factors for $ariable 'li$e'loa s an material properties. Ao e recommen ations for weight of permanentmaterials ' ea loa ' are also conser$ati$e# but not as conser$ati$e as for li$eloa s.


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)or a specific member# rearrangement of framing members is one wa! tore uce esign loa s. 2se of lighter-weight materials within thebuil ing shoul also be consi ere if feasible.

)or repetiti$e members such as floor &oists# esign loa can be re uce b!

using re uce spacing. This ma! allow for re uction of &oist epth. ,owe$er#net cost for all the &oists remains effecti$el! the same or greater# ue toincrease labor costs.

Support Aon itions )or beam elements such as floor &oists# one relati$el! simple wa! to re uce

eflection is to use continuous elements that span o$er one or more interiorsupports# in a ition to the usual support at or near each en . ,owe$er#continuous beams result in con itions that must be carefull! e$aluate .

Deflection *f Simpl! Supporte Beam

beam with two supports one at each en is t!picall! escribe as a single-span or 'simpl! supporte ' beam. )or uniform loa w along the entire beam#ma%imum eflection at mi span is calculate b! the stan ar formula Deflection# mi span inches C 5 w =;3 / 83


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>ow consi er a beam with three supports# forming two separate spans# witheach span ha$ing the same length = as for the simpl!-supporte beam in thepre$ious e%ample. This beam is continuous o$er the center support# such that there is no &oint in

the beam as there is when two separate beams are use .

)or the same uniform loa w use for single-span# simpl! supporte beamapplie to both spans of the two-span continuous beam# ma%imum eflectionfor each span is onl! 0.3 in e% $alue # which is 3 -percent of the baseline$alue 1.00 . Eust as for the simpl! supporte beam# this $alue is applicable

separatel! for uniform ea loa # uniform li$e loa # an total loa .

,owe$er# we must consi er a separate loa case# when li$e loa is applie toonl! one of the two spans. )or this case# ea loa eflection remains thesame while ma%imum li$e loa eflection in the one span increases to 0.70

70-percent of li$e loa eflection for simpl! supporte beam . *ther loa ing con itions such as point loa s must also be consi ere .,owe$er# a continuous beam ten s to re uce ma%imum eflectionssignificantl!# using the same beam size as for two single-span beams. Therefore# use of two-span continuous beam ma! allow for re uction in beammoment of inertia an beam size. The following results of using a two-span beam must be consi ere

FF +reater reaction force at center support compare to two single-spanbeams . )or two-span beam# with e"ual spans# reaction force is 5-percentgreater than total combine reaction force for two single-span beams ofsame total length . This affects esign of whate$er element ma! be pro$i ingthe center support# such as a separate gir er# as well as foun ation walls anfootings. FF )or greatl! une"ual span lengths one span much longer than the other #uplift reaction force ma! occur at outer en of shorter span for li$e loa on thelonger span onl!. 4f such uplift can not be resiste # eflection of the longerspan woul be increase greatl!. lso# upwar mo$ement will usuall! be

unacceptable# especiall! for a buil ing.

Aantile$er Metho for Multi-Span Beam =ine

)or a line of beams with multiple supports# eflection can be re ucecompare to simpl!-supporte beams spanning between supports almost as

much as for continuous beams b! using the cantile$er metho . This metho


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eliminates the nee for moment-resisting connections which are often re"uirefor continuous beams.

Aonsi er the simple case of two spans on three supports# which are oftencolumns A1# A # A . *ne beam B1 can be e%ten e cantile$ere o$er the

interior support A . The secon beam B then spans from insi e en of B1to the thir support A . Aonnection between B an B1 is a simple hinge-t!pethat resists shear onl!.

4nsi e en of B1# at en of the cantile$er segment# is esignate 91 for furtheriscussion. 9oint 91 eflects ownwar ue to loa from B . ,owe$er# 91eflects upwar ue to loa on B1 between supports A1 an A . >et eflection

ma! therefore be upwar # epen ing on loa ing con itions.

s long as the net cantile$er segment of B1 is not e%cessi$e# the followinga $antages result# compare to using two beams that span between supports

1 Moment an eflection of B is less since span length of B has beenre uce . ,owe$er# eflection of an! point on B # relati$e to each support A

A must inclu e net eflection of point 91 at en of B1 . )or li$e loa s onB onl!# li$e loa eflection of point 91 will be ownwar .

Deflection of B1# between supports A1 an A # is re uce ue to point loafrom B at point 91# which causes upwar mo$ement of B1 between supports.

This basic esign concept can of course be use for multiple beams with morethan three supports.

design to minimize deflection

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