DESIGN OF STEEL STRUCTURES

Transcription

1 DESIGN OF STEEL STRUCTURES

2 Design of Compression Member A structural member carrying axial or eccentric compressive load is called compression member.

3 Types of compression member : The vertical compression member in RCC building is termed as column, where as for steel structure it is called stanchion. The compression member in roof truss or bracing is called as strut. The principle compression member in a crane is called p p p boom.

4 Boom

5 Mode of failure of column : Crushing Buckling Mixed of both Crushing failure: This type of failure occur in short column Such member has a critical load cause material failure. Buckling failure : This type of failure occur in long column Such member has a critical load which cause elastic instability due to which the member fail. Mixed mode of failure: The above two failure occur in the extreme cases. For all intermediate value of slenderness ratio the column fail due to combined effect. Most of the practical column fail in this mode.

6 Effective length (l eff ) : Itis the length between two adjacent Point of zero moments. Thus length depend upon end condition. From, IS 800 : 1984, Clause 5.. Where accurate frameanalysis analysis is not done, the effective length of a compression member in a given plane may be Determined ed by the eprocedure e given in Appendix C. However, in most cases the effective length in the given plane assessed on the basis of Table 5., would be adequate. Effective length as given in Table 5. may also be adopted where columns directly form part of framed structures.

7 β 1 β Kc K + c K b K b K c + K b K c Flexural Rigidity of column K b Flexural Rigidity of beam.

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10 Buckling failure : Euler s Theory Assumptions Made in Euler s Theory: The column is initially iti straight ht(it is not crooked) kd) The load acting passes through centerline (axial compression) The slenderness of column is high (Long column) The cross section of column is solid, with constant section throughout height of column The column material is homogeneous, isotropic, and elastic The boundary conditions are ideally met

11 From moment curvature relation : X P d dx M y Py M EI y Critical Load (P c ) Critical stress ( c ) π EI l eff Y f P π EI c cc, or, c A Al eff π E λ slenderness. Ratio( λ) l eff r

12 Column design formula Merchant Rankin formula 1 f n 1 f n cc f 1 f + n y cc y f 1 ( n n f + f ) n In WSM method of design cc Axial compression strength ( ac ) 0.6 f For different grade of steel, ac is given in Table 5.1 f y n 1.4

13 # A built up column consists of two ISMC400@49.4Kg/m And two plates of size 500x10 mm. the clear distance Between back to back of channels is 00 mm. one plate Is connected to each flange side. Determine the safe load Carry capacity of the section if the effective length of the Column is 5 m. Sol: Properties of ISMC 400: 400 Thickness of web ( t w ) 8.6 mm Thickness offlange flange (t f ) 15.3mm Cross section area of the section(a st ) 693 mm Moment of inertia along X X axis (I xx ) 15088x10 3 mm 4 Moment of inertia along Y Y axis (I yy ) 5048x10 3 mm 4 100

14 For built up section: I xx mm mm I min 3 { } I yy Minimum radius of gyration: Imin rmin A 136.6mm

15 Slenderness Ratio ( ) : l eff 5000 λ r min From IS 800 : 1984, Table 5.1, Pg 39 ac MPa Safe load for the section (P) P A ac KN ( ) N

16 Bending stress : If compression flange is restrained laterally against buckling then permissible compressive or tensile bending stress is (Clause 6..1, Pg 55) bc / bt 0.66 f y For unrestrained compression flange (Clause 6..3) bc f f ( ) 1 n n f + f n cb f cb Elastic critical stress in bending (Clause 6..4) f bc K 1 cb ( X K Y ) C C y y 1

17 Where, Y X 6. 5 Y l r 1 y MPa 1 0 l τ r D r y τ MPa K 1 t f t w, or, t D or h Coefficient( K ψ A 1 A 1 ) f ( ψ ) C1, C respectively the lesser and greater distances from the section neutral axis to the extreme fibers. A 1 Total area of both flanges at the point of least bending moment. A Total area of both flanges at the point of maximum bending moment.

18 Coefficien t( K ) f ( ω ) ω I yy, cf I yy, f I yy,cf Moment of inertia of the compression flange alone. I yy,f Momentof of inertia of the both flangesabo about titso own axis parallel to the y y axis of the girder,.

19 Bending compression strength bc For different grade of steel, bc is given in Table 6.1A to F

20 Combined Axial Compression and Bending : From IS 800 :1984, Clause 7.1.1, Pg 90 Members subjected to axial compression and bending shall be proportioned to satisfy the following requirements: ac, cal C mx bcx, cal C my bcy, cal ac 1, 1, ac cal ac cal bcx 0.6 bcy f ccx 0.6 f ccy C m β β 0.85 M min M max Sway frame or Non sway with ends are restrained against rotation. tti Non sway and not subject to transverse loading Non sway with ends are unrestrained against rotation

21 If ac, cal, < 0.15, then ac ac, cal ac, cal ac + + bcx bcx, cal bcx, cal + + bcy bcy bcy, cal, cal At support we can use following equation 0.6 f y bcx bcy Combined Axial Tension and Bending: 0.6 at, cal f y + btx, cal 0.66 f y + bty 0.66, cal f y 1.0

22 # Design a steel column for the loading as shown in figure as per IS 800 :1984, steel lis Fe50. Sol : Effective length for the propped cantilever column (l eff ) l eff 0.8 l 4. 8 m 80 KN B 5 KN/m 6 m Total Axial Load ( selfwt. + 80) ( ) KN 88KN Maximum bending moment is at support A is : A M A wl KN 8 8 m

23 Let s assume, ac/bc 80MPa Thus, Required sectional area and sectional modules of the column is: A Z req A.L M ac A req bc 80 Try with ISMB300@44.Kg/m 1100 mm 8150 mm 3 Check for axial compression: ac, cal MPa

24 Slenderness ratio ( λ ) l eff < 180, OK r 8.4 min From IS 800 :1984, Table 5.1, Pg 39 Permissible axial compression stress is : ac 36.6MPa > ac, cal, Check for bending tension : 6 M A.5 10 bt, cal Z xx OK MPa 0.66 f 165 MPa >, OK bt 0 y bt, cal

25 Check for bending compression : 6 M A bc, cal Z xx MPa For, ISMB300@44.Kg/m h t f λ t t f w < 7.5 d < t w D τ 1.4 l r eff yy

26 From IS , Table 6.1B, Pg 58 D/Γ L eff / r y bc MPa > bc, cal, OK Combined Axial Compression and Bending check: ac, cal 15.64MPa, ac 36. 6MPa bc, cal 39.MPa, bc MPa

27 For, Radius of Gyration along X X axis: r xx 13. 7mm π E π 10 f λ 38.8 From interaction formula λ xx l eff 5 cc, xx ac, cal ac < C mx r bcx xx MPa, cal ac, cal bcx 0. 6 f cc, xx , OK

28 # Design a steel compound column for the loading as shown in figure as per IS 800 :1984, steel is Fe KN Sol Effective length for the column (l eff ) 8 m l eff l 16 m Assume slenderness ratio ( ) 100, ac 80 MPa λ so A l eff r l eff , rreq 160 mm Required Radius of λ 100 Gyration P req 1500mm Required Sectional Area ac 80

29 Let s try with X ISHB350@67.4Kg/m r xx 149.3mm, A 8591mm 50 I xx I yy mm 4 mm 4 S For I xx I yy S mm 140mm slenderness ratio (λ) λ { S } l r eff xx < 180, OK

30 From IS 800 :1984, Table 5.1, Pg 39 ac 75MPa 3 P ac, cal 58.MPa < A 1718 ac, OK For compound column we have to provide either Batten or, Lacing : Design of Lacing: It behave like truss member and will be under tension or compression. Single Lacing. Double Lacing.

31 IS 800 :1984, Clause 5.7.5, Pg 51 Let s θ C r yy { 40 0, 70 0 } 0 < 50 C θ or, < 0.7 λ column ryy Radius of gyration of column element

32 Width of Lacing Bars. (IS 800, Clause 5.7.3, Pg 50) In riveted construction, the minimum width of lacing bars shall be as follows: Let s Assume rivet diameter 0 mm Lacing width 75 mm. Thickness of Lacing Bars. (IS 800, Clause 5.7.4, Pg 50) Minimum thickness of Lacing : l t 40 For Single Lacing l length between l 60 For Double Lacing inner ends of rivets.

33 d ( S 15) ( ) 155mm d 19. mm Thus, Minimumrequired thickness l mm Let s provide 8 mm thick Lacing d Design force taken by Lacing (IS 800, Clause , Pg 48).5 V.5% of, P KN 100 d

34 FSin KN F KN Minimum radius of Gyration: 1 3 I 75 8 min r 1 min. 31mm A 75 8 F F KN λ d r min < 145, OK From IS 800 :1984, Table 5.1, Pg 39 ac ac 85. 1MPa 3 F ac, cal MPa < A ac 75 mm, OK

35 Check in axial Tension: Gross diameter of rivet (ф) φ mm Net sectional area of the lacing: ( ) 8 48mm A net Thus, Tensile stress in the lacing: 3 F at, cal 0.65N / mm < A 48 net 8 ac ( 150N / mm )OK,

36 For Thickness of flange ( t f ) 11.6 mm Thickness of Lacing ( t ) 8 mm Rivet value of the 0 mm diameter rivet: Single shear strength value π 100 π V τ av φ KN Bearing strength value 300 P pt φ t Thus Rivet value (R) 36.3 KN F 8.84 Minimum i No. of rivet to be Number of rivet 0. 4 R provided is, in each side 36.3 KN

37 Batten: It behave like very small beam member and Subjected to bending moment. The effective length of battened column should be increased dby 10%. Minimum 4 No. of batten should be provided. Provided batten on opposite faces such that one should be the mirror image of other. Thickness of batten (t) is same order of thickness of flange. t C r yy S 50 < 50 or, < 0. 7 λ column d S C d e

38 Longitudinal shear (V 1 ): VC V 1 NS V Transverse shear force (.5% of P) N The number of parallel planes of battens V A 1 av, cal τ av batten Longitudinal Moment (M): M τ VC N ( 0.4 f ) y bt M ( 0.66 f ), cal bc, cal bc Z batten / bt y

39 Design of Flexural Member A beam is a structural member subjected to transverse load, i.e load perpendicular to the longitudinal axis.

40 Types of beam (Based on end condition ): Simply supported Overhanging Cantilever Fixed beam continuous Propped cantilever

41 Typical name of beam : Joist : A closely spaced beam supporting floors or, roof of Building but not supporting the other beam. Larger beam are used for supporting a number of joists. They are called Girders. Beam are also used to carry roof loads in trusses. These Beam are called Purlins. Stringer : In building, beams supporting stair steps, in bridges a longitudinal beam supporting deck floor and Supported by floor beam.

42 GIRDER

43 Spandrel beam : In a building a beam on the outside Perimeter of a floor, supporting the exterior walls and Outside edge of the floors. A horizontal beam spanning the wall columns of industrial Building used to support wall coverings is called a GIRT. A roof beam usually supported by purlins is called a Rafter. Beam are also used to support the loads from the masonry Over the openings. Such types of beam are called Lintels. Floor beam: A major beam supporting other beams or Joints in a building; also the transverse beam in bridge.

44 LINTEL

45 Mode of failure of beam : Primary mode of failure of beams are as follows : Bending failure : Due to crushing of compression flange or fracture of tension flange. Shear failure : Due to buckling of web near location of high shear force. Dfl ti fil St t i d t b fil Deflection failure : Structure is assumed to be fail or unsuitable if excessive deflection occur.

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47 # Design a steel beam for the loading as shown in figure as per IS 800 :1984 Maximum bending moment wl 60 6 M max 70KN 8 8 From IS , Clause 6., Pg 55 m Permissible stress in Bending Tension/ Compression( bt/bc ) 0.66 f y For Mild steel f 50 MPa y 165 MPa bt bc 165

48 Thus, Let s start with bc 100 MPa bc Required section modulus ( Z ) M bc 7 Let s try with ISMB 1.6 Kg/m 10 5 mm 3 6 Self wt. of section 1.6 KN/m Ttll Total load d(dl+ll) 61.6 KN/m Maximum bending moment: M max Z xx mm wl KN m 8 8

49 Check for bending tension : bt, cal 90.06MPa < 165MPa OK Check for bending compression : For ISMB 600 Thickness of flange ( t f ) 0.8 mm Thickness of web ( t w ) 1.0 mm t t f w < d < t w 85

50 From IS , Table 6.1B, Pg 58 h D t τ 0.8 f λ l eff r y < 180 D/Γ , OK L eff / r y bc MPa

51 Bending stress due to load : bc cal 90.06MPa < , bc Check for shear stress : τ av 0.4 f y 100MPa (95.548) So, section is safe Vmax KN 3 Vmax τ av. cal 5.51MPa < τ av (100 MPa h tw So, section is safe )

52 Check for web crippling : Crippling is to be checked under point load or support only. From IS 800, clause 6.3, Pg 68 Maximum Bearing strength ( p ) 0.75f y MPa For continues support Calculated bearing stress : p, cal 40.47MPa < MPa ( ) For S. Support

53 Check for web buckling: Crippling is to be checked under point load or support only. Web buckling is critical at N.A. and crippling is critical where the Web start to be straight. From, IS , Clause , Pg 87 Slenderness ratio of web: λ d t w 1 From IS 800, Table 5.1, Pg 39 3 ac 110MPa

54 Calculated axial compression stress : 3 Vmax MPa < 110 Bt ( ) ac. cal ac w ( MPa ) So section is safe Check for deflection dfl : 4 5wl Deflection due to load ( δ cal ) 384 EI From Clause , Pg 34 Permissible value of deflection mm Span mm > δ cal