1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 10 Torsion, Shear, and Flexure

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1 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Maahe Inie of ehnolog Oline.54/.54 Mehani and Deign of Conree Srre (3--9) Oline orion, Shear, and Flere orion o Sre diribion on a ro eion bje o orion τ ma : narrow ide : wide ide o Maimm hear re, τ ma τ η ma η hape faor, orqe,, dimenion of he ro eion. he hape faor i differen for linear and nonlinear ae. / 8

2 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline Failre mode o orion failre of plain onree or ddenl wih an inlined enion rak in one of he wider fae, hen eending ino he narrow fae. Conree rhing or in he oppoie wider fae. orional rengh, p, of plain onree o Several heorie have been preened for omping orional rengh of plain onree inlding elai, plai, and kew bending heorie. o Skew bending: w M π 4 b i he applied orqe and M, w, are he bending and wiing momen, repeivel, on he 4 π plane. M, b, ( ) S 6 3 p σ M 3 p S, 3 limae orion for plain onree when σ reahe σ. p p 3 σ ( ) σ.85 f f 6 f r / 8

3 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline r 6 p f f 3 orional rengh onribed b eel o Conider he em oniing of longidinal and ranvere (irrp) eel: (, are he dimenion of eel frame a hown.) π 4 o orional momen wih repe o ai of he verial irrp ( α ) A f A area of one irrp leg, f irrp re, and irrp paing. o orional momen wih repe o ai of he horizonal irrp ( Aα f ) o oal orional momen Af ( α α ) + Af α (α i deermined from eperimen.) 3 / 8

4 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline Deign onep o oal limae orion apai, + orional apai onribed b onree, and orional apai onribed b reinforemen. β ( β.4 ) h, p.8 f he oeffiien β repreen redion in orional rengh provided b onree afer raking. Upon raking of onree re and rain are pariall ranferred o eel. Siffne and rengh of he em will depend on he amon of ranvere and longidinal reinforemen. o he final failre ma be in one of he following wa:. Under reinfored Boh ranvere and longidinal eel ield before failre.. Over reinfored Conree rhe before ielding of eel. 3. Pariall over (nder) reinfored o For nder reinfored elemen, α i independen of he eel raio. α Af 4 / 8

5 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline o Code ggeion: α Role of longidinal eel. I anhor he irrp, parilarl a orner.. I provide dowel reiane. 3. I onrol rak widening. Condiion of nder reinforemen A A l A l + volme per lengh of longidinal eel. Seel ield fir. orion ombined wih flere orion ombined wih hear o Generall hear ei imlaneol wih bending. he eiene of hear will rede he reiing abili in orion. h, i i neear o onider he ae of orion ombined wih hear. o For RC beam wih ranvere reinforemen: Pre orion: + Pre hear: / 8

6 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline ACI Code o Deign for orion Same ineraion a in member wiho ranvere reinforemen. o Ee orqe Over and above ha reied b onree, he ame amon of reinforemen i provided in member bje o orion pl hear a wold be reqired for prel orional member. hi orional reinforemen i added o ha reqired for arring bending momen and fleral hear. o φ φ( + ) n faored orqe, φ apai redion faor for orion.75, n nominal rengh for orion, orional momen arried b onree, and orional momen arried b eel. o + hear..8 f pre orion and f bd pre.4 bd.4 and C bd C o Ame, h ha 6 / 8

7 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline.8 f.4 + C, fbd +.5C α Af, φ ( ) + φ n A fd v A φ φ ( φ ) α f αφ f o 4 i reqired o are ielding of eel fir. o Minimm paing of orional irrp 4( ) + or in. Condiion of negleing orional effe o orional effe ma be negleed if n.5φ i i ( ) < f i n ) ( i i m of he mall reangle for irreglar hape. i Hollow eion h 7 / 8

8 .54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Oline o When h >, onider he ro eion a olid. 4 o When h 4 o When, ame i a olid b mlipl ( ) h < b 4 h., onider i a a hin-walled eion. Chek for inabili (loal bkling). General formlaion of po-raking behavior of flere, hear, and enion ineraion in R/C beam Diion of appliaion: Conree gidewa em from monorail and maglev ranporaion infrarre. Deign Eample Shear and orion 8 / 8