Comparison of the Design of Flexural Reinforced Concrete Elements According to Albanian Normative

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1 ISBN Proceedings of 2015 Interntionl Conference on Innovtions in Civil nd Structurl Engineering (ICICSE'15) Istnbul (Turkey), June 3-4, 2015 pp Comprison of the Design of Flexurl Reinforced Concrete Elements According to Albnin Normtive Igli Kondi 1, Julin Kshrj 1 nd Elfrid Shehu 1 1 Deprtment of Civil Engineering, Fculty of Civil Engineering, Polytechnic University of Tirn, Albni i.kondi13@gmil.com; jkshrj69@yhoo.c; elfridl@yhoo.com Abstrct: In this work, the uthors present the findings obtined from the nlysis of clculting the bering cpcity of reinforced concrete elements under the bending moment. The chose element, reinforced concrete bem, is designed ccording to Albnin Normtive with two methods, llowble stress design method nd limit stte design method. Furthermore, is mde comprison between the nlysis results. In the beginning presenttion is mde with the theoreticl solution of the problem nd fter tht the comprison is bsed on numericl solution. The conclusions re followed from the recommendtions given in the end of this work. Keywords: llowble stress design method, limit stte design method, design of flexurl elements, Albnin Normtive 1. Introduction The design of reinforced concrete structures, in different time periods, is performed in ccordnce with pproved technicl normtive, using three methods [1] llowble stress design method or clssic method rupture method limit stte design method In yers of the lst century, in Albni, the llowble stress design method ws used for the design of motorwy or rilwy bridges nd lso for the design of hydro technicl structures where the crcking where not llowed. The rupture method ws used for the design of industril nd civil buildings. The limit stte design method ws used without restrictions for reinforced concrete structures nd lso for the prestressed concrete structures. This method is the one tht is used ctully in our country. The comprison of the results of the clcultion of the bering bending moment of the sme element ccording to the two methods, shows the usge dvntge of the limit stte design method ginst llowble stress design method. 2. Design Methods of Reinforced Concrete Elements According To Albnin Normtive Symbols According the Two Methods The symbols between { } belong to the llowble stress design method. Only the symbols tht differ re shown. The sme symbols re not shown. A s reinforcing steel re on the tensile zone; {F } A sc reinforcing steel re on the compression zone; {F } R s design strength of reinforcing steel A s ; {R } 155

2 R sc design strength of reinforcing steel A sc ; Usully R s = R sc becuse the sme steel is used; {R ; usully R =R } σ s reinforcing steel stresses on the tensile zone; {σ } σ s reinforcing steel stresses on the compression zone; {σ } E s reinforcing steel modulus of elsticity; {E } 2.2. Allowble Stress Design Method In Albni this is the first nd the oldest method nd for this reson is lso known s the clssic method. This method is bsed on the elstic phse of work of concrete nd the reinforcement, so it does not use the plstic cpbility of mterils. The hypothesis where this method is bsed: ccept nd use formuls of the construction science Accept the Bernul s hypothesis, which do not ccept the deformtion of cross section but only the rottion or movement of the cross section. Concrete in tensile zone mke no conctribution. All the stresses in the tensile zone re hold only by the reinforcing steel. Stresses chrt in the compression zone is of tringulr liner shpe. See Figure 2.1. Convert the reinforced concrete element (concrete + reinforcing steel) in only concrete element. For this reson, the reinforcing steel re is multiplied by number n, where n = E /E b. E nd E b re respectively reinforcing steel modulus of elsticity nd concrete modulus of elsticity. Consider the reinforced concrete s homogenous nd isotropic mteril Bsed on the bove hypothesis, the stress distribution on the reinforced concrete element with reinforcing steel in tensile nd compressive zone under the bending moment, with cross section symmetric ginst the verticl xis, is given in Figure 2.1. Fig. 2.1: Stress distribution ccording the the llowble stress design method In Figure 2.2 is showed the stress distribution in n element with rectngulr cross section. σ b constrins of concrete in the compression zone D b equivlent force in the compression zone Fig. 2.2: Stress distribution in rectngulr cross section ccording to the llowble stress design method. Given the hypothesis where this method is bsed [1]: F ek = F b + n F + n F (2.1) F b = b h (2.2) 156

3 Sttic moment ginst rndom xis: Moment of inerti ginst rndom xis: The bsic eqution tht shows the essence of this method is: S ek = S b + n S + n S (2.3) I ek = I b + n I + n I (2.4) Action Bering cpcity (2.5) As ction will be the bending moment, sher force, etc. The respective bering cpcity is lso bending moment, sher force, etc. It depends from the llowble stresses in concrete [σ b ], from the llowble stresses in the tensile reinforcing [σ ], from the llowble stresses in the compressed reinforcing [σ ], from element s cross section dimensions (b nd h), from the re of tensile reinforcing (F ) nd the compression reinforcing (F ). In cse of bending the eqution (2.5) is written: Controls tht re crried out: Acting bending moment Bering bending moment (2.6) σ b = M x / I ek [σ b ] (2.7) σ = n σ b = n M (h 0 x) / I ek [σ ] (2.8) If condition (2.7) is fulfilled, thn condition (2.9) lso is lwys fulfilled: σ = n M (x ) / I ek [σ ] (2.9) To determine the position of the neutrl xis we strt from the fct tht the sttic moment ginst it should be equl to zero. In view of figure 2.2 we cn write: From where: Moment of inerti: x = 0.5 b x 2 + n F (x ) n F (h 0 x) = 0 (2.10) ' n (F F ) 1 b I ek = b x 3 3 n F (h ' 2 b (F h 0 F 1 ' 2 n (F F ) 0 x) 2 ' ') n F (x ') 2.3. Limit Stte Design Method According to Albnin normtive [7] we hve three limit sttes: 2 (2.11) (2.12) Ultimte limit stte Servicebility limit stte ccording to deformtion Servicebility limit stte ccording to crcking Ultimte limit stte clcultions hve to be lwys performed. Clcultions for other two limit sttes my be performed in specil occsions, where is seen resonble. Hypotheses used re [7]: Plnr cross sections under the bending moment rotte, but remin plnr. Concrete works only in the compression zone. Concrete stress chrt in compression zone is ccepted constnt. Stress vlues re equl to the concrete compression strength, R b. There is no contribution from the concrete in bering the stresses in tensile zone. Only the reinforcing steel work in tensile zone. Stresses in reinforcing steel re R s. If there is reinforcing steel in compression zone, the stresses in it re R sc. Strins in reinforcing steel nd in the concrete in its vicinity re the sme. Ultimte reltive strin in compression for concrete is 0.2%. Bsed on the bove hypothesis, the stress distribution on the reinforced concrete element with reinforcing steel in tensile nd compressive zone under the bending moment, with cross section symmetric ginst the verticl xis, is given in Figure

4 Fig. 3.1Stress distribution ccording limit stte design method The determintion of the position of the neutrl xis is mde by following equtions: where R b in N/mm 2. x y = ξ y h 0 (3.1) ω ξ y = (3.2) ω For hevy concrete: ω = R b (3.3) For light concrete: ω = R b (3.4) If x x y, then there is no need for A sc, so A sc = 0. If x > x y, then A sc is needed, so A sc 0. In this cse there is risk for compression zone filure. To void this cse A sc is used. Clcultion in cse where there is no need for A sc, (x x y, A sc = 0). According to figure 3.1 we cn write two equilibrium equtions. Clcultion in cse where there is no need for A sc, (x > x y, A sc 0). According to figure 3.1 we cn write two equilibrium equtions. M = A b R b z b (3.5) A s R s A b R b = 0 (3.6) M = A b R b z b + A sc R sc z s (3.7) A s R s A b R b A sc R sc = 0 (3.8) Design of reinforced concrete elements with rectngulr cross section (x x y, A sc = 0). Stress distribution is shown on figure 3.2. Fig. 3.2: Stress distribution in rectngulr cross section ccording to the limit stte design method From (3.5) we hve: Lets write ξ = x / h 0. Substituting on (3.9): From eqution (3.10) find A 0 : M = b x R b (h x) (3.9) M = b h 2 0 R b A 0 (3.10) A 0 = ξ (1 0.5 ξ) (3.11) 158

5 M A 0 = 2 b h 0 R b (3.12) ξ = 1 (1 2 A 0 ) 1/2 (3.13) x = ξ h 0 (3.14) If x clculted from eqution (3.14) x y, determined from eqution (3.2), then from eqution (3.6) we cn find A s : A s = ξ b h 0 R b / R s (3.15) Design of reinforced concrete element with rectngulr cross section (x > x y, A sc 0) Let see gin figure 3.2. To mximlly utilize the compressed zone of concrete we ccept x = x y = ξ y h 0. Eqution (3.7) cn be writte: After some trnsformtions we hve: From (3.8) we hve: M = b x y R b (h x y ) + A sc R sc (h 0 ) (3.16) A sc = M A R sc 0y b h (h ' ) R b (3.17) A oy = ξ y (1 0.5 ξ y ) (3.18) A s = A sc + ξ y b h 0 R b / R s (3.19) 2.4. Results of the Clcultions of Flexurl Reinforced Concrete Elements Numericl exmple 1 A bem under flexurl ction is nlyzed. Rectngulr cross section with b = 30cm nd h = 50cm, = = 3.5cm, h 0 = h = = 46.5cm. According to llowble stress design method concrete is of mrk M 300 (cubic resistnce), [σ b ] = 135dN/cm 2 ; steel Ç.5, [σ ] = 1600dN/cm 2 ; n = E / E b = 10. According to limit stte design method the concrete is of clss B30 (cubic resistnce), R b = 160dN/cm 2, E b = dN/cm 2 ; steel Ç.5, R s = 2400dN/cm 2, E s = dn/cm 2 ; n = E s / E b = A sc (F ) = 0cm 2 ; A s (F ) = 4φ16 = = 8.04cm 2. Determine, with the two methods, the flexurl strength of the bem. ) Allowble stress design method. With help of eqution (2.11) determine x = 13.33cm. With help of eqution (2.12) determine I ek = cm 4. With help of eqution (2.7) determine the bering moment M = dN cm. With help of eqution (2.8) determine the bering moment M = dN cm. Finlly the bering moment is the smllest between those tht re determined from (2.7) nd (2.8). In this cse dn cm b) Limit stte design method. With help of eqution (3.6) determine x = (A s R s ) / (b R b ) = 4.02cm. With help of eqution (3.9) determine the bering moment M = dN cm. With limit stte design method, the bering moment results 58% greter. Numericl exmple 2 A bem under flexurl ction is nlyzed. Rectngulr cross section with b = 30cm nd h = 50cm, = = 3.5cm, h 0 = h = = 46.5cm. According to llowble stress design method concrete is of mrk M 300 (cubic resistnce), [σ b ] = 135dN/cm 2 ; steel Ç.5, [σ ] = 1600dN/cm 2 ; n = E / E b = 10. According to limit stte design method the concrete is of clss B30 (cubic resistnce), R b = 160dN/cm 2, E b = dN/cm 2 ; steel Ç.5, R s = 2400dN/cm 2, E s = dn/cm 2 ; n = E s / E b = A sc (F ) = 2φ10 = 1.57cm 2 ; A s (F ) = 4φ16 = = 8.04cm 2. Determine, with the two methods, the flexurl strength of the bem

6 ) Allowble stress design method. With help of eqution (2.11) determine x = 12.56cm. With help of eqution (2.12) determine I ek = cm 4. With help of eqution (2.7) determine the bering moment M = dN cm. With help of eqution (2.8) determine the bering moment M = dN cm. Finlly the bering moment is the smllest between those tht re determined from (2.7) nd (2.8). In this cse dn cm. b) Limit stte design method. With help of eqution (3.8) determine x = (A s R s A sc R sc ) / (b R b ) = 3.23cm. With help of eqution (3.7) determine the bering moment M = dN cm. With limit stte design method, the bering moment results 86% greter Clcultions, Anlysis, Results To mke possible the comprison of the clcultion results, the elements re considered in the sme conditions. The sme clss of concrete nd steel is ccepted, the sme quntity of reinforcing steel (compressed nd tensile), the sme cross section dimensions. Grphiclly is showed the connection between the bering bending moment nd other fctors s: width of cross section, height of cross section, concrete llowble stresses, steel llowble stresses, E S /E b rtio, quntity of tensile reinforcement, quntity of compressed reinforcement. ) b) c) d) e) f) 160

7 g) Fig. 5.2: Reltionship between bering bending moment nd different fctors, ccording to llowble stress design method. ) b) c) d) e) f) Fig. 5.3: Reltionship between bering bending moment nd different fctors, ccording to limit stte design method

8 Fig. 5.4: Reltionship between bering bending moment nd cross section width, method comprison. Fig. 5.5: Reltionship between bering bending moment nd cross section height, comprison method Fig. 5.6: between bering bending moment nd tensile steel re, method comprison Fig. 5.7: Reltionship between bering bending moment nd compressed steel re, method comprison 3. Conclusions In ll the cses the bering moment strength, clculted with the limit stte method (L.S) is higher compred to tht clculted with the llowble strength method (A.S.D). This is n expected result knowing tht the L.S use better the contribution of concrete nd of the reinforcing steel in the elstic phse. See ll the figures, specificlly figures 6.3 to 6.6. With the incresing of cross section width b lso the bering moment is incresed. Si figure 6.3. The digrms re lmost prllel. The impct of b is equl to both the methods. Impct of b in the bering moment is smll. A 2.5 time increse of width bring 4% increse of the bering moment, clculted with both the methods. With the incresing of cross section height h lso the bering moment is incresed. See figure 6.4. Impct of h is more significnt in the L.S method; the respective digrm is more inclined. Impct of h in the bering moment is greter. An increse of 1.75 time of height brings 95% increse in the bering moment ccording to L.S nd 87% ccording to A.S.D. With the incresing of tensile reinforcing re F (A s ) lso the bering moment is incresed. See figure 6.5. Ultimte bering moment ccording to A.S.D depend from llowble stresses in concrete. Green digrm correspond to the bering moment connected with the llowble stresses in the reinforcing steel. Compring this digrm with tht of L.S method, result tht the impct of the tensile reinforcement is more significnt in the L.S method. The respective digrm is more inclined. The impct of the quntity of tensile reinforcement is high. An increse of 4.84 time the re of reinforcement bring pproximtely 4.5 time increse ccording to L.S nd 4.3 time ccording to A.S.D of the bering moment. With the incresing of compressed reinforcement F (A s ) lso the bering moment is incresed. See figure 6.6. The digrm is lmost prllel. The impct of F (A s ) is lmost equl for both the methods

9 The impct of the quntity of compressed reinforcement is high. An increse of 4.84 time the re of reinforcement bring pproximtely 4.5 time increse ccording to L.S nd 4.3 time ccording to A.S.D of the bering moment. Bering moment clculted with L.S method does not depend from n. The dependence of the bering moment from the concrete llowble stress, clculted with A.S.D method, is complicted becuse the moment depends lso from n See figure 6.1c. According to Albnin normtive n=10 for concrete mrk < 200 nd n=15 for concrete mrk 200. Lst three dots in figure 6.1c digrm correspond to the first three dots of the digrm in figure 6.2c. Is seen tht lso in this cse the vlues of bering moments clculted ccording to L.S method re higher. As conclusion we cn sy tht the trnsition from the llowble stress design method to the ultimte stte method, for design from bending moment, ccording to Albnin normtive, for the flexurl reinforced concrete elements, brings decrese of the quntity of reinforcing steel nd concrete, decresing the cost. 4. References [1] NEGOVANI K., VERDHO N. - Teori e ndërtimeve prej betoni të rmur, Vëllimi I-rë, Tirnë, 1973 [2] NEGOVANI K., VERDHO N. - Konstruksione prej betoni të rmur, Vëllimi II-të, Tirnë, [3] MINISTRIA E NDËRTIMIT E REPUBLIKËS SË SHQIPËRISË - Kushte teknike të projektimit, Librt 1 deri 23, Tirnë, [4] MINISTRIA E NDËRTIMIT E REPUBLIKËS SË SHQIPËRISË - Kusht teknik projektimi për ndërtimet ntisizmike KTP - N.2-89, Tirnë, [5] VERDHO N., MUKLI G. - Shembull numerikë në konstruksionet prej betoni të rmur, Vëllimi I-rë, Tirnë, [6] VERDHO N., MUKLI G. - Shembull numerikë në konstruksionet prej betoni të rmur, Vëllimi II-të, Tirnë, [7] VERDHO N., MUKLI G. - Konstruksione prej betoni të rmur, Pjes I-rë, Tirnë, [8] I.S.T.N. Kusht teknik i projektimit të konstruksioneve b.. me metodën e gjendjeve kufitre, K.T.P. N.30, [9] I.S.T.N. Kusht teknik mbi simbolet në b.., K.T.P. N.28, [10] GHERSI A. - Il cemento rmto, Plermo, [11] BIONDI A. - Cemento rmto, Ctni,