: A STUDY IN THE MECHANCAL BEHAVIORS OF THE RC BEAM WITH LARGE RECTANGULAR OPENING UNDER A POINT LOAD : : : : :
: ABSTRACT In ig-rise uiding consrucion passing service ducs and pipes roug openings in e foor eam eiminaes a significan amoun of dead space or e of e uiding and susania consrucion cos saving can e reaized. However incuding openings in e we of a reinforced concree eam e mecanics eavior of e eams wi openings are quiey difference from e eams wiou openings u ere are no corresponding specificaions in e curren code ye. Based on e easic anaysis a design meod is proposed on e simpe suppored eams wi arge recanguar openings under a poin oad. Six eams designed y e proposed meod were esed. Tes resus indicaed a e meod is saisfacory. On e Sudy of e eams wi opening we undersand e easic mecanics eavior y means of e easic finie eemen meod and pooeasic experimen. Tes of e six eams verified e easic anaysis. Simuaion cacuaion is carried ou y noninear finie eemen meod. Te resued of FEM mee we wi e es resus and e eoreica resus. Te pracica design meod presened in is paper may e referenced for an engineering ecnician. Keyword: reinforced concree; eam wi openings; cord; easic anaysis; inerna force; design meod
...........4......6.....6.....6.....8......9......9........4........5......5.......5.......7.................................5.......5......7........ 4...... 4......6 4......8
4......8 4.....4 4.....48 4..4...49 4..5...5 4..6...5...54 5....54 5....54 5.....54 5.....55 5....57 5.4...58...6 6....6 6....6...64
/ 66. : ; ; ; ; ( )
/ Lorensren [] T ( ) Nasser Karim W. [] Barney George B. [] 8 T : ( ) Mansur [4][5] : : 66
/ ( M N ) Kennedy [6] 4 Dougas [7] 9 von Mises Poo [8] 986 [9] [] [] T [] T [] 9 [4][5] 66
/ 4 66 (..)V. () ;() ;() :() : () :
/ () : 5 66
/. Ngo Scordeis 967 Swanson Anaysis Sysem Agor Srucura Researc & Anaysis ADINA Engineering AB G+D Compuing Eurosim/Mecaog Agor SAP 5 6 ADINA SAP9 ADINA SAP9 ADINA. SAP SAP9 SAP9 4. 6 66
/ [K s] e : [ K s ] e = c AE cs L c cs cs s cs s c cs c cs cs s cs s ( ) A L E c=cos s=sin -. 4-4 xoy ; o = = - [7][8][9] : e T [ K ] = [ B] [ D][ B] dxdy ( ) c [B] [B] T dxdy - + 4 : [ K c ] e = - T [ B] [ D][ B] J dξdη ( ) 7 66
/ [8] (-) :[B] [B]=[B B B B 4] B N x = N y i i i N i y N i x J ; [ J ] x ξ = x η y ξ y η [D] ν E [ D] = ν ν ( ν / ) E. [] : SAP9 ADINA ; ADINA 4 Oosen f 8 66
/ 4 f > f y E si=f y E s(i-)/f y(i-) E s(i-) f y(i-) E s(i-) (f y-f y(i-))/f yi< -5.. (-). 4 (-) (-). [K] e [K] e =[K c] e +[K s] e (-4) [K c] e [K s] e.. ADINA E- (Oosen ) - Oosen - - -. Oosen : 9 66
/ J J I f ( I J θ ) = A + λ( θ ) + B = ( 5) f f f c c c AB ( ) ( = ) ( ) - ( ) : K cos[ arccos( K cosθ )] λ( θ ) = π K cos[ arccos( K cosθ )] ( 6) K K 4 4 4 : f c f f c 4 : f /f c A B K K.8.874 4.96 4.486.995..758.96.768.98..98.5969 9.9.9647 66
/. -4 ( ) = / ( ) ( f f) -4 P( ) OP F( f f) : σ β = σ f σ = σ f = OP OF ( 7) < = >. Saenz -5 () OA : =E (-8) () OC : σ = E + ( R + E s Eε ε ε )( ) (R )( ) ε ε E σ ( ) E σ u R = s ( ε u ) ( ε u ) ε ε ε + R( ) ε ( 9) E s= / 66
/ ; u u () CB ( ) (-9) B 4. -5 --.. : d d d [ ] D c = d d d d 44 d 55 d 66 ( ) d = d = d νe = c ( + ν )( ν ) d = d = d E ( ν ) = c ( + ν )( ν ) d 44 = d 55 = d 66 E c = ( +ν ) : : E c--- ; ---. : 66
/ 66 d d d 66 (-) - D cf : [R] : i n i m i(i=). ( -5CB ) E= E u..4. [ ] ) ( 66 55 44 ' = d d d d d d d d d d d d D cf η η η [ ] [ ] [ ][ ] ) ( ' = R D R D cf T cf [ ] 4) ( + + + + + + + + + = n n m n n m m m n n m m n n n m n m m m n n m m n n n m n m m m n n m m n m n m n m n n m m n m n m n m n m R
/ 4 66 ADINA - -6. ADINA RTOL : 5) ( + + + F R RTOL F R i ( ) ETOL : 6) ( ) ( ) ( () ) ( ) ( + + + F R u ETOL F R u T i T i o P -6
/ SAP9 9. SAP9 : a e e - - L=5mm =48mm =8mm 78 96.. -. -(a) 5 66
/ - a e TB 65 6 6 6 8 TB 65 4 4 8 TB 65 4 8 TB4 8 6 6 6 8 TB5 8 4 4 8 TB6 8 4 8 TB7 95 6 6 6 8 TB8 95 4 4 8 TB9 95 4 8 TB 65 6 8 TB 65 8 8 4 TB 65 6 8 - TB 65 8 8-4 TB4 65 4 4 7 TB5 65 4 4 6 TB6 65 4 4 9 TB7 65 4 4 TB8 65 6 7 TB9 65 6 9 TB 65 6 7 - TB 65 6 9 -. () 6 66
/. ;... B C A D A A C C C A - B C A D A A C C TB4 TB5 TB6 TB7 TB8 T9-4 TB5 TB8(TB -) B C A D 7 66
/ A A C C TB TB4 TB7 TB TB6 T9 Y= / Y TB TB9 Y TB TB TB TB T e e A C B D ; a. x xy -5 x x : x x B C A D A C x 8 66
/ e ( TB) x Y e ( TB) B D A C x ( TB6) x xy : xy xy. 9 66
/ 66... : ) ( ) ( ) ( = + + + = = + y x y x y x y x σ σ σ σ E G. ( ) ( ) : P H P M ---- L H L M----- H M----- ) ( ) ( = = M M M M H H H H L P L P σ σ
/ σ H σ M PH LM M PH LM = = = k PM LH H PM LH ( 4) H=k M (-5).. ( ). 9 / 45 5-6 (e =) TB TB4 TB6 ; (e =mm) TB TB8 TB9 ; ( e =-mm) TB TB TB. ; 5 / =/5-7 66
/ 49- WZB-4..7MPa 49- -6-7 66
/... -8 4 5 7 8 (a) TB () TB (c) TB4-8 ( ) 66
/. - =nf(n F N/cm ) Tresca -9 TB Tresca* ( = =) WBZ-4 ( ) - TB I-I o o o - 4 66
/ - TB TB TB TB4 TB6 TB8 TB9 TB TB o /.4.4.4.46.4.45.4.44.44 o /.4.4.44.45.4.4.4.44.4. - B D B D... 5 66
/ - N V M N V M M V z : N = N = N V + V = V M + M + Nz = M ( a) ( ) ( c) ( 6) x/ =/4//4 5 - - - 4-4 5-5 - TB x x x xy 6 66
/ N= xdy V= xydy M=... - (kn) - - 5-5 V V V /V V V V /V V 5 V 5 V 5 /V 5 V /V TB 8.98 9.6.499 8.98 9..499 8.984 9..499.5 TB 8.98 9.4.499 8.98.9.499 8.984 8.978.5.5 TB 8.99 9.9.5 8.99 8.968.5 8.989 9.7.499.5 TB4 8.977 9..499 8.98 9.9.499 8.98 9..499.5 TB5 8.98 9..499 8.978 9.8.499 8.987 9.6.499.5 TB6 8.989 9.4.499 8.99 9.4.499 8.987 9..499.5 TB7 8.969 9..498 8.97 9.7.498 8.97 9..498.5 TB8 8.975 9..499 8.978 9.8.499 8.978 9..499.5 TB9 8.984 9.8.497 8.986 9.8.499 8.984 9.4.499.5 TB 6.5.947.6 6.55.94.6 6.5.947.6. TB.577 4.47.99.575 4.4.99.57 4.47.99.65 TB.889 6.79.66.9 6.9.66.9 6.79.66.689 TB 4.45.595.8 4.47.6.8 4.44.595.8.85 TB4 9.7 8.987.5 9.4 8.98.5 9. 8.984.5.5 TB5 9.4 8.96.5.94 8.968.5 9.4 8.959.5.5 TB6 8.95 9.6.495 8.957 9.47.498 8.948 9.49.497.5 TB7 8.96 9.94.495 8.96 9.86.496 8.9 9.95.495.5 TB8 6.49.96.4 6.8.9.8 6.79.9.8. TB9 6..977.5 6..98.5 6..979.5. TB.95 6.5.664.94 6.55.664.945 6.5.664.689 TB.889 6.4.66.89 6.9.66.889 6..66.689 - - - 5-5 P=5kN 7 66
/ V 8kN V V : V = kv = V = V δ δ ( + ) + δ δ δ ( 7) V == kv = V = V δ δ ( + ) + δ δ δ ( 8) :.. () ( ) < : δ = δ = ; GA GA () ( ) 4. : δ = + EI GA. δ = + ; EI GA () ( ) > 4 : δ = δ = ; EI EI () - A = A = + I = I = =. G=.4E δ = ; E δ + = E : δ + ( / ) = δ + ( / ) ( 9) 8 66
/ (-9) (-7) (-8) : V V V = = δ + + ( / ) δ + ( / ) + V = V V ( ) (-) (-) V /V -. -4 (kn) (kn m) - - (-6) N N M M N N M M o / o / o / o / TB 4.75 4.756.84.87 4.75 4.76.54.55.4.4.45.45 TB 4. 4..9.5 4. 4.4.4.48.44.44.44.44 TB 8.89 8.89.9.6 8.85 8.8..5.46.46.46.46 TB4 4.7 4.7.5.5 4.79 4.557.649.658.4.4.46.46 TB5 4.95 4.94.49.4 4.95 4.95.477.49.45.45.455.455 TB6 8.774 8.777.57.5 8.774 8.78.5.6.47.47.47.47 TB7 4.69 4.695.7.5 4.697 4.697.5.544.44.44.448.448 TB8 4.68 4.64.54.59 4.7 4.7.4.66.46.46.464.464 TB9 8.75 8.749.669.66 8.75 8.75.8..47.47.476.476 TB 4.7 4..75. 4. 4.9.9.569.45.4.454.4 TB 9.48 9.48.48.7 9.48 9.48.98.89.46.4.465.4 TB 4.8 4...74 4.5 4..557.98.4.45.4.454 TB 9.476 9.479.85.48 9.479 9.54.876.99.4.46.4.465 TB4 5.98 5.9.55.44 5.5 5.8..5.45.45.445.445 TB5.49.4.4.79.47.44.5.94.46.45.449.449 TB6 45.76 45.78.965.964 45.78 45.76.78.94.44.4.46.46 TB7 5.45 5.49.94.9 5.45 5.45.4.44.4.4.4.4 TB8 5.89 5.98.74.89 5.7 5.98.7.499.46.44.457.49 TB9 45. 45..689.5 45.9 45.7.5.645.45.4.45.46 TB 5. 5.4.5.74 5.6 5.6.487.7.44.46.49.457 TB 45.58 45.58.6.69 45.58 45.6.6.4.4.44.46.45 9 66
/ TB~TB 5 (-6 a) -4 - - (.4~.47) - - - Va : Va Va : y : ( y ) I I Va Va : ( y ) : ( y ) I I :y ; I ; I = I + y + I + y ( ) : N =N : Va y I Va Va Va + ( y ) = ( y ) + ( y ) I I I + : y = ( ) ( + ) (-) (-) : I = I + I + + ( + ) ( ) Va Va y I I : ( y ) V = I o 66
/ 66 : ) 4 (.5 = o a I I V V : ) 5 (.5 = o a I I V V (-4) : I /I o ; a/ o ; a a/ o ; V/V o -4 (-) V/V (-) I (-4) (-5) : o a + + + + + + + = ) / ( ) / (.5 o a + + + + + + + = ) / ( ) / (.5 : o c a c c + + = -4 c c c :
/ 66 = = 6) ( ) (.5..5 ) (.5..5 a a a o o -4 (-6) : 7) (.5.5 + + + + = = = o o V V M N N N : M M =V(a- /)
/ 4.. - - :TB TB TB4 TB5 TB TB4 4-. 55# C 4-4- (kg) (mm) C.5-- 7 558 7 ( f cu 5 5 5mm mm) 4-4- 4- ( ) (Mpa) ( 4 Mpa) TB 5 9.. TB 5.7.5 TB4 55 6.6.45 TB5 55 6.5.85 TB 55 7.4.94 TB4 54 4..6 66
/ 4 66
/ 5 66
/ 4- (MPa) (MPa) ( 5 Mpa) (%) 6.5 479..7 8 446.9 6.9 6 459. 7. 7 549.7 7.5 6 7 555.7 7.5 85 579. 6. 6 59..8 4.. : ; ; ;. 5 IMP ( ).mm --5mm 4 BX-AA A mm... % 4- / 5 6 66
/ () 5 4-4- () 4-4 7 66
/ 4. 4.. 4-5 8 66
/ 9 66
/ TB: C B B 6 C 8 A D 7 8.6Pu A.8.9Pu B 5 TB: TB C B 8 5 5 TB4: C B B C..4Pu A D.6Pu 4 66
/.8.9Pu TB5: C B B C..4Pu A D.6Pu TB: C B D.6Pu A.8.9Pu 5 TB4: C B..4Pu D.6Pu 8.8.9Pu TB TB TB4 TB5 C ( ) 8 B 4 66
/..4Pu A D.8.9Pu TB TB.6Pu TB TB4 TB5 TB TB4 TB TB5 TB TB TB TB TB4 TB4 TB TB4 A C -8 4.. 4 66
/. () TB TB4 TB.FEM TB.FEM TB4.FEM TB (XkN) (XkN) TB4 TB TB TB.FEM TB.FEM TB4.FEM -5-5 - 5 (µ ε ) 4-7 (µ ε ) 4-8 4-6 (a) () (c) A B (d) A B A B 4-7 4-8 A B 4 66
/ -- 4-6(c) TB TB4 () (XkN) 5 5 5 5 TB TB TB4 (XkN) 5 5 TB TB TB.FEM 5 TB.FEM TB.FEM TB.FEM TB4.FEM TB4.FEM 5 5 5 5 5 5 5 (µ ε ) (µ ε ) 4-4- TB4 44 66
/ 4-9 (a) () (c) C D (a) D (d) C D D C C D -- 4-4- () TB TB4. () 4-4- 4-4 -- 45 66
/ (kn) 5 5 5 TB (kn) TB TB. FEM 5 TB. FEM 5 5 (µ ε ) 4-5 5 5 TB TB4 TB. FEM TB4. FEM (µ ε ) 4-4 () 4-5 4-6 4-7 46 66
/ (XkN) 5 5 5 5 TB TB TB. FEM TB. FEM 5 5 (µ ε ) 4-6 XkN) 5 5 5 TB TB4 TB. FEM TB4. FEM 5 5 (µ ε ) 4-7. (XkN) 5 (XkN) 5 5 5 TB TB TB TB 5 TB4 5 TB4-4 9 4-4 9 (µ ε ) (µ ε ) 4-9 4-4-8 TB TB 47 66
/ TB4 4.. 4- : 48 66
/ (XkN) 5 5 5 5 TB.FEM TB TB4 TB5 (kn) 5 5 5 (mm) 4- TB.FEM TB4 TB TB ( mm) 4-4-4 4-4- ( ) mm L /5 4..4 4-4 P cre /P U P cr /P UE P UE /P U P UD (kn) P cre (kn) P cr (kn) P UE (kn) E (%) D (%) TB 8 5 4.9 8..8.9 TB 5 75 49..4..9 TB4 8 47. 8.9.4.8 TB5 8.4 9.88 9.5.96 TB 8 6. 9.5 7.. TB4 5 75 6.8 9.48 8.4.6.96.6. 49 66
/ 4-5 P cr 8.4% 9.5% 8.9%.4% 8.9% 9.6% 4-5 ( 4-4-) 4-5.9..98..4.9 P crf /P cr P UF /P U P UF /P U P cre (kn) P UE (kn) P crf (kn) P UF (kn) E E D TB 5 4.9 5 85...95.8 TB 5 49. 7.5.68.9.7 TB4 47. 9 7.5.95.96. TB5.4 6.5.8.5. TB 6. 9 7..95..9 T4 5 6.8 7 4..68.9.4 T4 5 6.8 7 4..68.9.4 4..5.8.9Pu 5 66
/ 4..6. 4-4 TB4 TB5 4- TB4 TB5 TB4 TB5 4-5 TB kn (a) () ( ) 4-6 4-7 TB5 TB4 (.44.5).8Pu (.48.5) (.5.47) 5 66
/.8Pu (.6.44) 4-6 ( o / ) TB TB TB4 TB5 TB TB4 P(kN) o / P(kN) o / P(kN) o / P(kN) o / P(kN) o / P(kN) o / 5.47.49.44.48.45.44.5 8.5 8.48 6.5 6.47 8.49 8.5 5.5 5.5.5.49 5.49 4.5.5.5 6.5 6.48.49 4-7 ( o / ) TB TB TB4 T P(kN) o / P(kN) o / P(kN) o / P(kN) o / 5.4.8.8.47.45 8.4 8.9 6.44 8.45 5.4 5.5.4 4.44.4.6 6.4 (-6). (-) 4-8 4-8 ( TB) 5 66
/ (-) (-) 4-8 V V V V /V - 7:V /V / (kn) (kn) (kn) TB 9.8 66. 4.6.6.5. TB 89.7 5. 9.6.56.5. TB4 89. 6.8 8..68.5.6 TB5 7.9 5.8..7.5.4 TB 78. 7. 5.7.5.. TB4 95. 5.5 44.5.5.5.6 5 66
/ [] ( ) 5. :. [4] ;. ;. ; 4. ; 5. ; 6. 5. 5.. :. : 54 66
/ M f cmx( -x/)+f y A s ( -a s ) : x x a s. : V A sv.7 f c +.5 f yv + s.8 f y A s sinα. Asv V f c +.5 f yv +.8 f y As sinα s λ +.5 s. 5... 5- s () : (-) : V = δ + δ V = V V V = + ( / + + ( / V ) ) () : (-6) : 55 66
/ o o a =.5. a =.5..5.5 () : (-7) : N M =V(a- /). :. Asv V o f c +.5 f yv o +. 7N λ +.5 s : V V.5 of c; = o/ N>. f c N=. f c :. Asv V o f c +.5 f yv o. N λ +.5 s : V V.5 of c; = o/ M + V + V o o = N = N =.5 + +.5...N > o f c.n = o f c λ +.5 λ +.5. : M =( - o)v (N M ) A s A s ξ = f cm N o 56 66
/ A s N e ξ (.5ξ ) f f y ( o ' a ) cm o > N ξ f cmo ξ = + ξ Ne.45 f cmo + f cm ' o (.8 ξ )( a ) o A s : ---- (d 5) =.544; e---- e=e i+.5 -a; e i---- e i=e o+e a e o=m o/n ; e a---- e a=.(. o-e o) e o. o e a= : A s A s4 (N M ) A s; (N M ) A s4 a x o x a x=a 5. ( 4-) 5-57 66
/ : = + 5-() 5-(c) v : δ v = E c V ( I cr + I cr ) :I cr I cr v [4][5] 5.4 : 5- [4] 4 L=mm =4mm =mm -.9..96 5- [5] P UE P UF (A) 5 (A A5) L=5mm; (B) (B B4) L=8mm - P UF P UE.85..9 58 66
/ 5- [4]4 a e d P UF P UE P UF/P UE R 4 8 4.9.9 R 6 8 7 8.5.94 R 8 8 44. 44.. R4 8 4..4.9 R5 8 99.4 4..95 R6 8 4 67 8.9 R7 8 9 9 4.9. R8 8 8-56 59..98 R9 8 8 9-74 74. R 8 8 8 7 77.4.96 R 8 8.5.5. R 8 8 45 54..94 R 8 8 75 5.4..9 R4 8 75 5 7. 76..96 5- [5] a e d P UF P UE P UF/P UE A 4 85 -- -- -- -- -- -- 6 45.95 A 4 85 58 8 4 9 56-7 6.5. A 46 8 57 4 5 48-6 5 5. A4 4 8 6 8 7 47 545 5 6 5 4. A5 44 9 58 8 5 4-6 95. A6 48 88 64 5.5 5.5 475 9 6 66 7.99 B 5 -- -- -- -- -- -- 76 475 5.89 B 5 6 7 8 785 5 76 446 46.97 B 5 98 6 9 6 75-4 76 45 5.88 B4 5 57 7 7 745 -.5 76 55 56.9 B5 5 6 9 5 755-76 47 57.6.89 B6 5 99 55 9 55 789-7.5 76 57 55.9 B7 5 95 6 68 8 76 7 76 55 589.89 B8 55 5 6 45 78 -.5 76 55 6.85 B9 5 96 6 5 7-5 76 48 55.9 B 5 6 85 55 77-5 76 5 557.4.9 B 5 5 6 8 765 5 76 47 5.9 B 487 96 5 57 7 6 64-5 76 49 577.4.85 B 55 8 65 78-6 76 5 58.4.86 B4 55 8 6 87.5 57.5 89-5 76 56 58.4.87 59 66
/ 5-5- 4-4 4.95 5- C C 5-5- P UF/P UD P UD (kn) P UD (kn) P UD (kn) P UF (kn) P UF/P UD P UF/P UD TB 5 8 9 85..8.98 TB 8 5.5.9.7. TB4 8 7.5.9.. TB5 8 8.5.8..9 TB 8 7..9. TB4 8 6 4..4.6 5 5-4 C C 5-4.44..9;.895.48.976 6 66
/ 5-4 P UF P UF/P UD P UD (kn) P UD (kn) (kn) P UF/P UD TB 8.5.5.964 TB6 8 96.89.9 TB7 8 8.56.99 TB8 8 9.67.94 TB9 8 88.44.895 TB 8..48 TB 8 4..5.97 TB 8.4..969 TB5 8 4.89.9 TB6 8 9.6.995 TB7 8.5.4.955 TB8 8.7.8. TB9 8..84.5 TB 8.67. TB 8..96 6 66
/ 6. :... / 4. 5. (-6) 6. (-) 7. 6.. T.. 6 66
/ 4. 6 66
/..LorensrenM. Hoes in Reinforced Concree Girders. Byggmasren V.4 No.7 Juy 96 p4-5(in Swedis).. Nasser Karim W.; Acavaos A.; and Danie H.R. Beavior and Design of Large Openings in Reinforced Concree Beams. ACI journa Proceedings V.64 No. Jan.967 p5-.. Barney George B.; Corey W. Gene; Hanson Jon M.; and Parmeee Ricard A. Beavior and Design of Presressed Concree Beams wi Large We Openings Presresed Concree Insiue Journa V. No.6 Nov.-Dec. 977 p-6. 4. Mansur M. A. Tan K.H. and Lee S. L. Coapse Loads of Reinforced Concree Beams Wi Large Openings Journa of Drucura Engineering ASCE V. No. Nov. 984 p6-68. 5. Mansur M. A. Tan K.H. and Lee S. L. Design Meod for Reinforced Concree Beams Wi Large Openings Journa of e American Concree Insiue V.8 No.4 Juy-Augus 985 p57-54 6. Kennedy J. B. and Adaa H. Saic Response of Presressed Girders wi Opnings. Journa of Srucura Engineering ASCE V.8 No. Fe. 99 p488-54. 7. Dougas T. R. Gamre S. C. Design of Beams wi Off-cener We Opnings. Journa of e Srucura of e Srucura Division ASCE V. No.ST6 June 974 p89-. 8. Poo R. B. and Lopes R. Cycicay Loaded Concree Beams wi We Openings. Journa of e American Concree Insiue V.8 No.5 Sep.-Oc. 986 p757-76. 9... :.. Vo. : 64 66
/ 994.6. p59-7.. : [ ]. : 995... :. : 998. p68-7.. T. 99. 4(): p78-85... 988(8): p- 4... 995. (): p6-4. 5.. : [ ]. : 998 6.. : [ ]. : 997 7... : 99. 8... : 994. 9... : 997.5. K J. ADINA/ADINT ----.. : 986..... : 987.9... : 995.5 65 66
/.. (GBJ -89). : 989. 4.. (GBJ 68-84). : 985. 5. Mansur M. A. Tan K.H. and Lee S. L. Defecions of Reinforced Concree Beams wi We Openings ACI Journa V.89 No.4 Juy-Augus 99 p9-97. 6. Te Join ASCE-ACI Tes Commiee 46 on Sear and Diagona Tension of e Commiee on Masonry and Reinforced Concree of e Srucura Division Te Sear Sreng of Reinforced Concree Memers Journa of Srucura Division ASCE V.99 No. S6 June 7 p9-85. 66 66