STEEL-CONCRETE COMPOSITE COLUMNS-I

Transcription

1 5 STEEL-CONCRETE COMOSITE COLUMNS-I 1.0 INTRODUCTION A steel-concrete composite column is a compression member, comprising either a concrete encased hot-rolled steel section or a concrete filled tubular section of hot-rolled steel and is generall used as a load-bearing member in a composite framed structure. Tpical cross-sections of composite columns with full and partiall concrete encased steel sections are illustrated in Fig. 1. Fig. shows three tpical cross-sections of concrete filled tubular sections. Note that there is no requirement to provide additional reinforcing steel for composite concrete filled tubular sections, ecept for requirements of fire resistance appropriate. b c c b c h c c hc b c b = b c (a) b h = hc h = hc (b) ( c ) Fig. 1: Tpical cross - sections of full and partiall concrete encased columns Copright reserved Version II 5-1

2 b d d h Fig. : Tpical cross-sections of concrete filled tubular sections In a composite column both the steel and concrete would resist the eternal loading b interacting together b bond and friction. Supplementar reinforcement in the concrete encasement prevents ecessive spalling of concrete both under normal load and fire conditions. In composite construction, the bare steel sections support the initial construction loads, including the weight of structure during construction. Concrete is later cast around the steel section, or filled inside the tubular sections. The concrete and steel are combined in such a fashion that the advantages of both the materials are utilised effectivel in composite column. The lighter weight and higher strength of steel permit the use of smaller and lighter foundations. The subsequent concrete addition enables the building frame to easil limit the swa and lateral deflections. With the use of composite columns along with composite decking and composite beams it is possible to erect high rise structures in an etremel efficient manner. There is quite a vertical spread of construction activit carried out simultaneousl at an one time, with numerous trades working simultaneousl. For eample One group of workers will be erecting the steel beams and columns for one or two stores at the top of frame. Two or three stores below, another group of workers will be fiing the metal decking for the floors. A few stores below, another group will be concreting the floors. As we go down the building, another group will be ting the column reinforcing bars in cages. Yet another group below them will be fiing the formwork, placing the concrete into the column moulds etc. The advantages of composite columns are: increased strength for a given cross sectional dimension. increased stiffness, leading to reduced slenderness and increased buckling resistance. good fire resistance in the case of concrete encased columns. corrosion protection in encased columns. Version II 5-

3 significant economic advantages over either pure structural steel or reinforced concrete alternatives. identical cross sections with different load and moment resistances can be produced b varing steel thickness, the concrete strength and reinforcement. This allows the outer dimensions of a column to be held constant over a number of floors in a building, thus simplifing the construction and architectural detailing. erection of high rise building in an etremel efficient manner. formwork is not required for concrete filled tubular sections..0 MATERIALS.1 Structural Steel All structural steels used shall, before fabrication conform to IS: , IS: , and IS: as appropriate. Some of the structural steel grade commonl used in construction as per IS: and IS: are given in Table 1. Table1(a): Yield strength f of steel sections Nominal steel grade Fe 570-HT Fe 540W-HT Fe 410-O (not subjected to dnamic loading other than wind) Nominal thickness/diameter (mm) Yield stress, f (Ma) t t t t t t t t t Table1(b): Yield strength f of steel sections as per IS 06:199 Nominal steel grade Fe 410W A Fe 410W B Fe 410W C Nominal thickness/diameter (mm) Yield stress, f (Ma) < > < > < > Version II 5-3

4 . Concrete Concrete strengths are specified in terms of the characteristic cube strengths, (f ck ) cu, measured at 8 das. Table gives the properties of different grades of concrete according to IS: and the corresponding EC4 values. Table : roperties of concrete Grade Designation M5 M30 M35 M40 (f ck ) cu (N/mm ) (f ck ) c (N/mm ) f ctm (N/mm ) E cm =5700(fck) cu (N/mm ) , (f ck ) cu characteristic compressive (cube) strength of concrete (f ck ) c characteristic compressive (clinder) strength of concrete, given b 0.8 times 8 das cube strength of concrete according to EC4 mean tensile strength of concrete f ctm For lightweight concrete, the E cm values are obtained b multipling the values from Table b /400, is the unit mass (kg/m 3 ).3 Reinforcing Steel Steel grades commonl used in construction are given in Table 3. It should be noted that although the ductilit of reinforcing bars has a significant effect on the behaviour of continuous composite beams, this propert has little effect on the design of composite columns. Concrete filled tubular sections ma be used without an reinforcement ecept for reasons of fire resistance, appropriate. Table 3: Characteristic strengths of reinforcing steel Tpe of steel Indian Standard Nominal size (mm) Yield Stress, f sk (N/mm ) Mild steel Grade I (plain IS:43(art1)-198 d0 50 bars) 0<d50 40 Mild steel Grade II (plain IS:43(art1)-198 d0 5 bars) 0<d50 15 Medium tensile steel IS:43(art1)-198 d (plain bars) 16<d <d Medium tensile steel (Hot-rolled deformed bars and Cold-twisted deformed bars) IS: for bars of all sizes Version II 5-4

5 Note: This chapter is confined to steel concrete composite columns made up of hot rolled steel sections having ield strengths within the range 50 N/mm to 350 N/mm and reinforcement with steel rods of 415 or 500 N/mm. This limitation is considered necessar at the present time on account of the lower ductilit of steels having higher ield strengths..4 artial safet factors.4.1 artial safet factor f for loads - The suggested partial safet factor f for different load combinations is given below in Table 4. Table 4 : artial safet factors ( According to proposed revisions to IS 800) Loading f DL LL WL Dead Load (unfavourable effects) Dead load restraining uplift or overturning Imposed Load + Dead Load Dead Load + Wind Load Dead Load + Imposed Load + wind Load (Major Load) Dead Load + Imposed Load (Major Load) + wind Load artial safet factor for materials The partial safet factor m for structural steel, concrete and reinforcing steel is given in Table5. Table 5: artial safet factor for materials Material m * Steel Section 1.15 Concrete 1.5 Reinforcement 1.15 *IS: Code for composite construction has prescribed m =1.15 for structural steel. (B contrast, EC4 has prescribed m =1.10 for structural steel). 3.0 COMOSITE COLUMN DESIGN 3.1 General As in other structural components, a composite column must also be designed for the Ultimate Limit State. For structural adequac, the internal forces and moments resulting from the most unfavourable load combination should not eceed the design resistance of Version II 5-5

6 the composite cross-sections. While local buckling of the steel sections ma be eliminated, the reduction in the compression resistance of the composite column due to overall buckling should definitel be allowed for, together with the effects of residual stresses and initial imperfections. Moreover, the second order effects in slender columns as well as the effect of creep and shrinkage of concrete under long term loading must be considered, if the are significant. The reduction in fleural stiffness due to cracking of the concrete in the tension area should also be considered. 3. Method of Design At present, there is no Indian Standard covering Composite Columns. The method of design suggested in this chapter largel follows EC4, which incorporates the latest research on composite construction. Isolated smmetric columns having uniform cross sections in braced or non-swa frames ma be designed b the Simplified design method described in the net section. This method also adopts the European buckling curves for steel columns as the basis of column design. It is formulated in such a wa that onl hand calculation is required in practical design. This method cannot be applied to swa columns. When a sufficientl stiff frame is subjected to in plane horizontal forces, the additional internal forces and moments due to the consequent horizontal displacement of its nodes can be neglected, and the frame is classed as non-swa. 3.3 Fire resistance Due to the thermal mass of concrete, composite columns alwas possess a higher fire resistance than corresponding steel columns. (It ma be recalled that composite columns were actuall developed for their inherent high fire resistance). Composite columns are usuall designed in the normal or cool state and then checked under fire conditions. Additional reinforcement is sometimes required to achieve the target fire resistance. Some general rules on the structural performance of composite columns in fire are summarised as follows: The fire resistance of composite columns with full concrete encased steel sections ma be treated in the same wa as reinforced concrete columns. The steel is insulated b an appropriate concrete cover and light reinforcement is also required in order to maintain the integrit of the concrete cover. In such cases, two-hour fire resistance can usuall be achieved with the minimum concrete cover of 40 mm. For composite columns with partiall concrete encased steel sections, the structural performance of the columns is ver different in fire, as the flanges of the steel sections are eposed and less concrete acts as a heat shield. In general, a fire resistance of up to one hour can be achieved if the strength of concrete is neglected in normal design. Additional reinforcement is often required to achieve more than onehour fire resistance. Version II 5-6

7 For concrete filled tubular sections subjected to fire, the steel sections are eposed to direct heating while the concrete core behaves as heat sink. In general, sufficient redistribution of stress occurs between the hot steel sections and the relativel cool concrete core, so that a fire resistance of one hour can usuall be achieved. For longer periods of fire resistance, additional reinforcement is required, which is not provided in normal design. Steel fibre reinforcement is also effective in improving the fire resistance of a concrete filled column. It is also a practice in India to wrap the column with ferrocement to increase the fire rating 4.0 ROOSED DESIGN METHOD The simplified method is formulated for prismatic composite columns with doubl smmetrical cross-sections. The calculations of various design parameters are covered and the checks for structural adequac of a composite column under applied loads are presented below. 4.1 Resistance of cross-section to compression The plastic compression resistance of a composite cross-section represents the maimum load that can be applied to a short composite column. Concrete filled circular tubular sections ehibit enhanced resistance due to the tri-aial confinement effects. Full or partiall concrete encased steel sections and concrete filled rectangular tubular sections do not achieve such enhancement Encased steel sections and concrete filled rectangular/square tubular sections:- p p ck p sk p h Fig. 3 Stress distribution of the plastic resistance to compression of an encased I section The plastic resistance of an encased steel section or concrete filled rectangular or square section (i.e. the so-called squash load ) is given b the sum of the resistances of the components as follows: p = A a.f / a + c.a c. (f ck ) c / c + A s.f sk / s p = A a.f / a + c.a c.[0.80* (f ck ) cu ] / c + A s.f sk / s (1) Version II 5-7

8 A a, A c and A s are the areas of the steel section, the concrete and the reinforcing steel respectivel f, (f ck ) c and f sk are the ield strength of the steel section, the characteristic compressive strength (clinder) of the concrete, and the ield strength of the reinforcing steel respectivel. (f ck ) cu the characteristic compressive strength (cube) of the concrete c strength coefficient for concrete, which is 1.0 for concrete filled tubular sections, and 0.85 for full or partiall concrete encased steel sections. For ease of epression, are presented as the design strengths of the respective materials such as p, p ck and p sk. Eqn. (1) can therefore be rewritten as follows: p = A a p + A c p ck + A s p sk ( ) At this stage it should be pointed out that the Indian Standards for composite construction (IS: ) does not make an specific reference to composite columns. The provisions contained in IS: are often invoked for design of composite structures. Etension of IS: to composite columns will result in the following equation: p = A a p + A c p ck + A s p sk (a ) f a, (f c ck c ) c and f sk s p = 0.87f ; p ck =0.4(f ck ) cu and p sk =0.67f (b) An important design parameter is the steel contribution ratio, a which is defined in EC4 as follows: Aa p a p (3) IS: is also to be emploed for the spacing and design of ties. Version II 5-8

9 4.1. Concrete filled circular tubular sections: Special rovisions The method described above is valid for rectangular and square tubular sections. For composite columns using circular tubular sections, there is an increased resistance of concrete due to the confining effect of the circular tubular section. However, this effect on the resistance enhancement of concrete is significant onl in stock columns. For composite columns with a non-dimensional slenderness of 0.5 ( is defined in Eqn.8,in section 4.3), or the eccentricit, e [defined in Eqn. 4 below], of the applied load does not eceed the value d/10, ( d is the outer dimension of the circular tubular section) this effect has to be considered. The eccentricit, e, is defined as follows: e M d 10 (4) e M is the eccentricit is the maimum applied design moment (second order effects are ignored) is the applied design load The plastic compression resistance of concrete filled circular tubular sections is calculated b using two coefficients 1 and as given below. t f p Aa p Ac pck 1 1 As psk (5) d fck t is the thickness of the circular tubular section. 1 and two coefficients given b 1 10 and 10e 1 d e d (6) (7) In general, the resistance of a concrete filled circular tubular section to compression ma increase b 15% under aial load onl when the effect of tri-aial confinement is considered. Linear interpolation is permitted for various load eccentricities of e d/10. The basic values 10 and 0 depend on the non-dimensional slenderness, which can be read off from Table 5. Non-dimensional slenderness is described in section If the eccentricit e eceeds the value d/10, or if the non-dimensional slenderness eceeds the value 0.5 then 1 =0 and = 1.0. Version II 5-9

10 Table 5: Basic value 10 and 0 to allow for the effect of tri-aial confinement in concrete filled circular tubular sections, as provided in EC 4 applicable for concrete grades ( f ck ) c = 5 to 55 N/mm Non-dimensional slenderness The plastic resistance to compression of a composite cross-section p, represents the maimum load that can be applied to a short column. For slender columns with low elastic critical load, overall buckling ma be critical. In a tpical buckling curve for an ideal column as shown in Fig. 4(a), the horizontal line represents p, while the curve represents cr, which is a function of the column slenderness. These two curves limit the compressive resistance of ideal column. For convenience, column strength curves are plotted in non dimensionalised form as shown in Fig. 4(b) the buckling resistance of a column ma be epressed as a proportion of the plastic resistance to compression, p thereb non-dimensioning the vertical ais of Fig. 4(a), is called the reduction factor. The horizontal ais ma be nondimensionalised similarl b cr as shown in Fig. 4(b). = / p p cr (/r) Slenderness ratio Fig. 4(a): Idealised column buckling curve p / cr Fig. 4(b) Non-dimensionalised column buckling curve Version II 5-10

11 ractical columns have strength curves different from ideal columns due to residual stresses and geometric imperfections. The European buckling curves have been drawn after incorporating the effects of both residual stresses and geometric imperfections. The form the basis of column buckling design for both steel and composite columns in EC 3 and EC4. For using the European buckling curves, the non-dimensional slenderness of the column should be first evaluated as follows: pu cr f E r f ( ) r (8) pu plastic resistance of the cross-section to compression, according to Eqn () or Eqn. (5) with a = c = s = 1.0 cr is the elastic buckling load of the column as defined in Eqn. (11). Once the value of a composite column is established, the buckling resistance to compression of the column ma be evaluated as given below Local buckling of steel sections Both Eqns. () and (5) are valid provided that local buckling in the steel sections does not occur. To prevent premature local buckling, the width to thickness ratio of the steel sections in compression must satisf the following limits: d t 85 for concrete filled circular tubular sections h t 50 for concrete filled rectangular tubular sections b 43 for partiall encased I sections (9) t f 50 f f is the ield strength of the steel section in N/mm (Ma). (10) For full encased steel sections, no verification for local buckling is necessar as the concrete surrounding effectivel prevents local buckling. However, the concrete cover to the flange of a full encased steel section should not be less than 40 mm, nor less than one-sith of the breadth, b, of the flange for it to be effective in preventing local buckling. Version II 5-11

12 Local buckling ma be critical in some concrete filled rectangular tubular sections with large h/t ratios. Designs using sections, which eceed the local buckling limits for semicompact sections, should be verified b tests. 4. Effective elastic fleural stiffness Composite columns ma fail in buckling and one important parameter for the buckling design of composite columns is its elastic critical buckling load (Euler Load), cr, which is defined as follows: cr EI e (EI) e is the effective elastic fleural stiffness of the composite column (defined in the net section). (11) is the effective length of the column, which ma be conservativel taken as sstem length L for an isolated non-swa composite column. However, the value of the fleural stiffness ma decrease with time due to creep and shrinkage of concrete. Two design rules for the evaluation of the effective elastic fleural stiffness of composite columns are given below Short term loading The effective elastic fleural stiffness, (EI) e, is obtained b adding up the fleural stiffness of the individual components of the cross-section: (EI) e = E a I a E cd I c + E s I s (1) I a, I c and I s E a and E s are the second moments of area of the steel section, the concrete (assumed uncracked) and the reinforcement about the ais of bending considered respectivel. are the moduli of elasticit of the steel section and the reinforcement 0.8 E cd I c is the effective stiffness of the concrete; the factor 0.8 is an empirical multiplier (determined b a calibration eercise to give good agreement with test results). Note I c is the moment of inertia about the centroid of the uncracked column section. E cd = E cm / * c (13) Version II 5-1

13 E cm * c is the secant modulus of the concrete, see Table of the tet. is reduced to 1.35 for the determination of the effective stiffness of concrete according to Eurocode. Note: Dividing the Modulus of Elasticit b m is unusual and is included here to obtain the effective stiffness, which conforms to test data. 4.. Long term loading For slender columns under long-term loading, the creep and shrinkage of concrete will cause a reduction in the effective elastic fleural stiffness of the composite column, thereb reducing the buckling resistance. However, this effect is significant onl for slender columns. As a simple rule, the effect of long term loading should be considered if the buckling length to depth ratio of a composite column eceeds 15. If the eccentricit of loading as defined in Eqn. 4 is more than twice the cross-section dimension, the effect on the bending moment distribution caused b increased deflections due to creep and shrinkage of concrete will be ver small. Consequentl, it ma be neglected and no provision for long-term loading is necessar. Moreover, no provision is also necessar if the non-dimensional slenderness, of the composite column is less than the limiting values given in Table 6. Table 6: Limiting values of for long term loading Concrete encased crosssections Concrete filled cross sections Braced Unbraced and/or swa Non-swa sstems sstems Note: is the steel contribution ratio as defined in Eqn. 3. However, when eceeds the limits given b Table-6 and e/d is less than, the effect of creep and shrinkage of concrete should be allowed for b emploing the modulus of elasticit of the concrete E c instead of E cd in Eqn. 13, which is defined as follows: E c E cd 0.5 d 1 (14) d is the applied design load. is the part of the applied design load permanentl acting on the column. Version II 5-13

14 The effect of long-term loading ma be ignored for concrete filled tubular sections with.0 provided that is greater than 0.6 for braced (or non-swa) columns, and 0.75 for unbraced (and/or swa) columns. 4.3 Resistance of members to aial compression For each of the principal aes of the column, the designer should check that p (15) p is the plastic resistance to compression of the cross-section, from Eqn. () or Eqn. (5) is the reduction factor due to column buckling and is a function of the nondimensional slenderness of the composite column. The European buckling curves illustrated in Fig. 4 (c) are proposed to be used for composite columns. The are selected according to the tpes of the steel sections and the ais of bending: curve a curve b curve c for concrete filled tubular sections for full or partiall concrete encased I-sections buckling about the strong ais of the steel sections (- ais). for full and partiall concrete encased I-sections buckling about the weak ais of the steel sections (- ais). = / p 1.0 a b c Fig. 4(c) European buckling curves pu cr Version II 5-14

15 These curves can also be described mathematicall as follows: 1 but 1.0 (16) 1( 0.) (17) 0.5 The factor allows for different levels of imperfections and residual stresses in the columns corresponding to curves a, b, and c. Table 7 gives the value of for each buckling curve. Note that the second order moment due to imperfection, has been incorporated in the method b using multiple buckling curves; no additional considerations are necessar. (It should be noted b wa of contrast that IS: for reinforced concrete columns specifies a cm eccentricit irrespective of column geometr. The method suggested here allows for an eccentricit of load application b the term. No further provision is necessar for steel and composite columns) Using the values of determined from Eqn. (8) and the reduction factor calculated from Eqn. (16), the design buckling resistance of the composite column to compression, b or p ma thus be evaluated. Table 7: Imperfection factor for the buckling curves European buckling curve a b c Imperfection factor The isolated non-swa composite columns need not be checked for buckling, if anone of the following conditions is satisfied: (a) The aial force in the column is less than 0.1 cr cr is the elastic buckling load of the column given b Eqn (11) (b) The non-dimensional slenderness, given b Eqn. (8 ) is less than STES IN DESIGN 5.1 Design Steps for columns with aial load List the composite column specifications and the design value of forces and moments List material properties such as f, f sk, (f ck ) c, E a, E s, E c Version II 5-15

16 5.1.3 List sectional properties A a, A s, A c, I a, I s, I c of the selected section Design checks (1) Evaluate plastic resistance, p of the cross-section from equation, p = A a f / a + c A c (f ck ) c / c + A s f sk / s () Evaluate effective fleural stiffness, (EI) e and (EI) e, of the cross- section for short term loading from equations, (EI) e =E a I a E cd I c + E s I s (EI) e =E a I a E cd I c + E s I s (3) Evaluate non-dimensional slenderness, and from equation, pu cr pu = A a f + c A c (f ck ) cu + A s f sk ( a = c = s = 1.0 ; Refer Eqn (8) ) cr pu cr EI e 1 1 EI e and cr (4) Check the resistance of the section under aial compression about both the aes. Design against aial compression is satisfied if following conditions are satisfied: < p < p Version II 5-16

17 and CONCLUSION 1 In this chapter the design of steel-concrete composite column subjected to aial load using simplified design method suggested in EC 4 is discussed. The use of European buckling curve in the design of steel-concrete composite column is described. The advantages of steel concrete composite column and the properties of materials used are also discussed. A worked eample illustrating the use of the above design procedure is appended to this chapter. NOTATION and A cross-sectional area b breadth of element d diameter, depth of element. e eccentricit of loading e o initial imperfections E modulus of elasticit (EI) e effective elastic fleural stiffness of a composite cross-section. (f ck ) cu characteristic compressive (cube) strength of concrete f sk characteristic strength of reinforcement f ield strength of steel (f ck ) c characteristic compressive (clinder) strength of concrete, given b 0.80 times 8 das cube strength of concrete. f ctm mean tensile strength of concrete p ck, p, p sk design strength of concrete, steel section and reinforcement respectivel I second moment of area (with subscripts) effective length L length or span aial force Version II 5-17

18 p plastic resistance to compression of the cross section. pu plastic resistance to compression of the cross section with a = c = s = 1.0 cr elastic critical load of a column c aial resistance of concrete, A c p ck t thickness of element Z e elastic section modulus plastic section modulus Z p Greek letters f m * c partial safet factor for loads partial safet factor for materials (with subscripts) reduction factor(1.35) used for reducing E cm value slenderness ( = non-dimensional slenderness) coefficient = 50 / f c c a s w d l imperfection factor strength coefficient for concrete reduction factor buckling reduction factor on aial buckling resistance b for long term loading steel contribution ratio, A a p / p reinforcement web of steel section dead load live load Note-The subscript, denote the - and - aes of the section respectivel. - denotes the major aes whilst - denotes the minor principal aes. Version II 5-18

19 Structural Steel Design roject Calculation Sheet Job No: Sheet 1 of 6 Rev Job Title: Composite Column Design Worked Eample: 1 Made B Date U Checked B Date RN ROBLEM1 Obtain plastic resistance of a steel section made of ISHB 50 encased in concrete. The height of the column is 3.0m and is pin ended m ISHB DETAILS OF THE SECTION Column dimension 350 X 350 X 3000 Concrete Grade M30 Steel Section ISHB 50 Reinforcement steel area Fe % of gross concrete area. Cover from the flanges Height of the column 50 mm 3000 mm Version II 5-19

20 Structural Steel Design roject Calculation Sheet Job No: Job Title: Sheet of 6 Rev Composite Column Design Worked Eample: 1 Made B Checked B U RN Date Date 5.1. LIST MATERIAL ROERTIES (1) Structural steel Steel section ISHB 50 Nominal ield strength f = 50 N/mm Modulus of elasticit E a = 00 kn/mm () Concrete Concrete grade M30 Characteristic strength (cube), (f ck ) cu =30 N/mm Characteristic strength (clinder), (f ck ) c =5 N/mm Secant modulus of elasticit for short term loading, E cm =310 N/mm (3) Reinforcing steel Steel grade Fe 415 Characteristic strength f sk = 415 N/mm Modulus of elasticit E s = 00 kn/mm (4) artial safet factors a =1.15 c = 1.5 s = LIST SECTION ROERTIES OF THE GIVEN SECTION (1) Steel section A a = 6971 mm Version II 5-0

21 Structural Steel Design roject Calculation Sheet Job No: Sheet 3 of 6 Rev Job Title: Composite Column Design Worked Eample: 1 Made B Date U Checked B Date RN h= 50 mm t w = 8.8 mm I a = 79.8 * 10 6 mm 4 I a = 0.1* 10 6 mm 4 () Reinforcing steel Area reinforcement = 0.5% of gross concrete area = 0.5/100 * ( 11559) = 578 mm rovide 4 bars of 14 mm dia., A s = 616 mm (3) Concrete A c = A gross A a -A s = 350 * = mm DESIGN CHECKS (1)lastic resistance of the section p = A a f / a + c A c (f ck ) c / c + A s f sk / s p = A a f / a + c A c (0.80 * (f ck ) cu ) / c + A s f sk / s = [6971 * 50 / * * 5 / * 415 /1.15]/1000 =3366 kn p = 3366 kn () Calculation of Effective elastic fleural stiffness of the section About the major ais (EI) e =E a I a E cd I c + E s I s I a = 79.8 * 10 6 mm 4 Version II 5-1

22 Structural Steel Design roject Calculation Sheet Job No: Sheet 4 of 6 Rev Job Title: Composite Column Design Worked Eample: 1 Made B Date U Checked B Date RN I s = Ah = 616 * [ 350/-5-7] = 1.6 * 10 6 mm 4 I c =( 350) 4 /1 [ ] *10 6 =1158 * 10 6 mm 4 (EI) e =.0 * 10 5 * 79.8* * 315 * * * 10 5 * 1.6 * 10 6 = 39.4 * 10 1 N mm E cd = E cm / * c =310 /1.35 =315 N/mm About minor ais (EI) e = 8.5* 10 1 N mm (3) Non dimensonal slenderness = ( pu / cr ) ½ Value of pu ( a = c = s = 1.0) pu = A a f + c A c (f ck ) c + A s f sk pu = A a f + c A c * 0.80 *(f ck ) cu + A s f sk = 6971 * * * * 616 = * 10 5 N ( cr ) = 4440 kn EI e (3000) 4307 kn 1 pu =4440 kn ( cr ) = 4307 kn Version II 5-

23 Structural Steel Design roject Calculation Sheet Job No: Sheet 5 of 6 Rev Job Title: Composite Column Design Worked Eample: 1 Made B Date U Checked B Date RN ( cr ) (3000) kN ( cr ) = 3154 kn ( ) ( ) (4) Resistance of the composite column under aial compression Buckling resistance of the section should satisf the following condition b < p b = buckling load = reduction factor for column buckling p = plastic resistance of the section = 3366 kn values : About major ais = 0.34 Version II 5-3

24 Structural Steel Design roject Calculation Sheet Job No: Sheet 6 of 6 Rev Job Title: Composite Column Design Worked Eample: 1 Made B Date U Checked B Date RN = 1 / { + ( - ) ½ } = 0.5 [1 + ( 0.) + ] = 0.5 [ ( ) + (0.30) ] = 0.57 = 1 / { [(0.57) (0.30) ] ½ } = About minor ais = 0.49 = 0.61 = ( b ) = = * 3366 =318 kn ( b ) = = * 3366 =3090 kn Hence, the lower value of plastic resistance against buckling, b = 3090 kn Lower value of plastic resistance = 3090 kn Version II 5-4