DESIGN OF STEEL STRUCTURES Design of slab and Gusset bases:
Slab Base or Base Plate: It is a steel plate placed between column base and concrete base. Area of Slab base σ P P Axial load in the column σ c - Permissible compressive stress in concrete c Concrete base 0 1 100 q θ tan 0.9 + 1 f ck where q 0 calculated maximum bearing pressure at the base of the pedestal in N/mm f ck characteristic strength of concrete at 8 days in N/mm. Slab Base
Thickness of a rectangular slab base t From, IS 800 : 1984, Clause 5.4.3, Pg 44 3 σ bs b w a 4 mm Slab base where t the slab thickness, in mm; w the pressure or loading on the underside of the base in MPa a the greater projection of the plate beyond column in mm b the lesser projection of the plate beyond the column in mm σ bs the permissible bending stress in slab bases ( for all steels, shall be assumed as 185 MPa ). a b b
Thickness of a square slab base under solid circular column: t 10 90W 16 B σ ( B d ) mm 16σ bs 0 where t the thickness of the plate, in mm. W the total axial load, in KN B the length of the side of cap or base, in mm σ bs the permissible bending stress in slab bases ( for all steels, shall be assumed as 185 MPa ) d 0 the diameter of the reduced end, if any, of the column in mm.
Gusseted base:
Grillage Foundation: It is provided at shallow depth for column carrying heavy Load on weak soil. It consists of two or more layers of steel Beams completely encased in concrete. The permissible stress in grillage g beam may be increased by 33.5% (50% in case of WL or EQ ). If the following condition are satisfied 1. The beam are unpainted and solidly l encased in ordinary dense concrete with 10mm aggregate and minimum f ck 15 Mpa.. Minimum distance between edge of flange is 75 mm. 3. Minimum concrete cover is 100 mm.
Design a grillage foundation for axial load 500 KN and in column section twoismc 50, withtwocovertwo Plates 300x5 mm. Minimum required width of slab base w 50 + 5 + 115 w 530mm Assume, w 600mm l w + 3h
Assume self weight of footing is 15% of axial load Total load 1.15x500 875 KN Z Area of bottom footing 875 50 11.5m Provide a 34 3.4x3.4m 34 grillage foundation Maximum bending moment. P ( L l ) M 8 500 (3.4 0.6) 875 8 6 M 875 10 3987 1.33σ 1.33 165 req bc KN 10 3 mm m 3 ISMB 450 Z 3987 10, 10 3 3 req each 139 3 mm 3 3.4 m
Try with ISMB450@7.4Kg/m C/Sarea required at criticalweb section A P 1.33 σ pt 500 1.33 10 189 3 9945.49 mm h 35. 4mm l 600 + 3 35.4 7. 6 mm Required total web thickness : ' A 9945.49 w 13. 67 mm l 7.6 If we provide 3 No of beam then web thickness of each beam w' 13.76 tw req 4.58 mm tw (9.4 mm ), OK, 3 3 <
Maximum shear force P( L l) 500(3.4 0.6) L 3.4 1030KN 6.03 10 τ av, cal 81N / mm < τ av (100 N / mm 3 450 9.4 1 ) Minimum required length of slab base 150 mm Thus. L 3 150 + 75 600 Let s provide 600 mm mm a 150 mm, b 150 Thickness of slab base, t 3 w a b σ bs 4 mm 3 500 10 w 6.94N 600 600 / mm t 43.58mm 4. 5cm
ROOF TRUSS: Rafter Pitch of roof truss h S Rise (h) Slope of truss θ Span (S) Bay : distance between adjacent truss. Eaves : the bottomedges of an inclined roof surface.
Load on roof truss: DL, LL, WL/SL Dead Load (DL) Weight of roof covering sheeting 150 N/m Weight of bracings 15 N /m From IS 875 II, Table Weight of purling 100 N/m Self Weight of truss Live Load (LL) 750 [( θ 10 ) 0 ] 1500 N / m Span ( m ) 10 + 5 N / m 3 N / m For Accessible roof 400 N / m If value of LL is less than 400 N/m then take LL 400 N/m Note: For truss analysis tk take LL as /3 of total t lll For purlins analysis take LL as total LL
Wind Load (WL): IS 875 III It depend upon wind speed and height of the structure. Basic Wind speed (V b ) It is determine on the based on statically Data of return period 50 year and at height 10 m above the ground Surface. Design wind speed (V z ) K 1 K K 3 V b K 1 Probability/Risk factor, depend upon class and design lifeofthe structure. Given intable 1
K Depend upon height, terrain category and class of the structure. Given in Table 3,3.
Class of structure If any maximum dimension of the structure (Length, width, height) < 0 m A, 0 50 m B, > 50 m C
K 3 Topographic factor, depend upon slope of ground wind flow direction. The effect of topography will be significant at a site when the upwind slope (θ) is greater than about t3 0, If slope of ground is less than 3 0 K 3 1, for other slope K 3 is Given in Appendix C Design Wind Pressure (P Z ) P Z 0.6 V Z N / mm Wind Load on Individual Members (F) F ( C ) pe C pi A e PZ C pe is external pressure coefficient (for Pitched roofs Table 5) C pi is internal pressure coefficient (clause 6..3) pi p ( ) A e effective area
Design an industrial shed for following dimension Span Length (m) Pitch of roof truss Spacing of truss (m) Location. Eaves Height (m) 8 0.5 5 Patna 6 Assume number of way is five. Draw plan view in scale Height of roof truss (h) h 0.5 8 m Effective area (A e ) A e 8 5 40m 5 m A e 8 m
Slope of the roof truss: m θ 4 1 tan 6.56 0 133 1.33 m Load calculation: 6 m Dead Load (DL) Weight of roof covering sheeting 150 N/m Weight of bracings15n/m 8 m Weight of purling 100 N/m 8 10 m 3 SelfWeight of truss + 5 76.67 N / Total DL intensity 341.67 N/m
DL A e 341.67 40 341.67 13666. 8N e Live Load intensity (LL) 750 [( θ 10 ) 0 ] 418.69 N / m 400 N / m Total LL on a truss Wind Load (WL): 3 418.69 40 Total DL+LL 4.83 KN 11165.3N Basic Wind speed for Patna (V b ) 47 m/s Design wind speed (V z ) K 1 K K 3 V b
Assume design life of the structure is 50 year So, K 1 1 Terrain category, Class of structure t B So, K 0.98 Slope of ground is less than 3 0 So, K 3 1 Design wind speed (V z ) 1x0.98x1x 47 46.06 m/s Design Wind Pressure (P Z ) 0.6x46.06 17.91 N/m Wind Force (F) ( C C ) pe pi A e P Z
External pressure coefficient on roof, IS 875 (III), Table 5 1 < w h 6 8 Case I, 0 0.75 Assume wall opening is less then 5% Internal pressure coefficient (C pi ) 0. Wind ward direction: < 3 6.56 0.7 0.5 0.37 10 ( C C ) pe pi max 0. 57 Lee ward direction 0.5 ( C ) pe C 0. 7 pi max Roof angle ( ) 6.56 0 Wind 0.37 0. 0.5
Case II, 0 0.8 0.731 Wind ward direction 0. 8 ( C C ) 1. 0 pe C pi max Lee ward direction: 6.56 0.6 + 0. 0.731 10 ( C ) pe C 0. 931 pi max 0. Wind Thus maximum value in all cases 10 1.0 Design wind load on roof truss (F) F ( C C ) A P 1.0 40 1.7 50. KN pe pi e Z 8
Truss analysis : Design load combination DL 13.67 KN, LL 11.16 KN, WL 50.8 KN P P I P H J G K DL + LL 4.38 KN Down ward P/ 4.38 P 4. 06KN 6 DL +WL 37.1 KN Upward P 37.1 P 6. 18 KN 6 P/ P A B C D E F P P P P P/ P/ P
analys sis: DL +LL Member Type Member Length (m) Forces (KN) Rafter Bottom Chord Vertical AG 1.486.7 Design force GH 1.486.7 in rafter is HI 1.486 18.15.7 KN IJ 1.486 18.1515 compressive JK 1.486.7 KF 1.486.7 AB 1.33 0.3 BC 1.33 16.6 DE 1.33 16.6 EF 1.33 0.3 CD.67 1.1 GB 0.664 4.06 EK 0.664 4.06 CH 1.39 6.087 DJ 1.39 6.087 BH 1.88 5.74 Diagonal JE 1.88 5.74 CI.4 7.31 ID.4 7.31
DL + WL analys sis: Member Type Member Length (m) Forces (KN) Rafter Bottom Chord Vertical AG 1.486 34.598 GH 1.486 34.598 HI 1.486 7.69 IJ 1.486 7.69 JK 1.486 34.598 KF 1.486 34.598 AB 1.33 30.94 BC 1.33 4.76 DE 1.33 4.76 EF 1.33 30.94 CD.67 18.59 GB 0.664 6.18 EK 0.664 6.18 CH 1.39 9.7 DJ 1.39 9.7 BH 1.88 8.74 Diagonal JE 1.88 8.74 CI.4 11.13 size of memb ber is ISA 50x50 0x6 Min nimum ID.4 11.13
Design of Purlins: It act as continuous beam 1.48 m Purlins Spacing of purlins 148m 1.48 1.33 m Weight of roof covering sheeting 150 x1.48 N/m Weight of purling 100x1.48 148 N/m Total DL 370 N/m LL 418.69 x 1.48 cos (6.56 0 ) 554.6 N/m WL 17.91x1.48 1883.9 N/m DL + LL 94.6 N/m DL +WL 1513.9 N/m Foe WL case permissible stress is increased by 33 %
If we considered permissible is same, we can take effective load in DL + WL case 1513.9 DL + WL 1138.7 N / m > DL + 1.33 LL (94.6 N / m ) Thus, Design load is DL + WL Maximum bending moment From, IS 456 : 000, Table 1 Continuous beam wl 1138.7 5 M 845. 67 N m 10 10 Z M 845.67 10 3 req 17.5 σ bc / bt 165 10 3 mm 3 5 m Minimum depth L/45, Width L/60
Design of Column DL + LL 4.38 KN Down ward Axial load on column 4.38 1.1919 KN DL +WL 37.1 KN Upward Wind C pi 0. Axial load on column 37.1 18.56KN Transverse load due to wind From IS 875 (III), Table 4 1 < h w 6 8 0.75 < 3, 3 < l w 5 8 3.15 < 4 ( C C ) 0 9 C pe C pi max 0. Transverse load intensity 0.9 5 17.91N / m 5.7 KN / m
Design column and Foundation for the load as shown 1.19 KN B 5.7 KN/m 6 m A
Radius of gyration and slenderness ratio : The radius of gyration is given by I I I xx yy r, r xx, r yy, rmin A A A Where, I Moment of inertia A Cross sectional area of the section I min A