Lecture 4 s.s. iii Design of Steel Structures - Faculty of Civil Engineering Iaşi
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This document discusses the design of transversal frames in steel industrial buildings. It covers: 1) Static schemes for analyzing the frame with either hinged or rigid connections between the column and truss. Rigid connections introduce redundancy effects. 2) Methods for determining the stiffness of frame elements like the truss and columns, which influences internal forces and moments. 3) Different loading schemes on the frame, including combinations of permanent, variable and temporary loads for design. 4) Analyzing internal forces and moments in the column for frames carrying crane girders. Simplified models are used. 5) Considerations for sizing the truss stiffness and determining redundancy effects on truss
Lecture 4 s.s. iii Design of Steel Structures - Faculty of Civil Engineering Iaşi
- 1. Lecture 4 STEEL INDUSTRIAL BUILDINGS C.Teleman.StelStructuresIII. Lecture4 1
- 2. dc d d dc c c KK K MM KK K MM ; 111 hMI N i M iii IIII 0 DESIGNOFTHETRANSVERSALFRAME Local effects of the fixing between column and truss: moments in the members of the truss Hinged connection Rigid connection
- 3. 1.STATICSCHEMES • Articulated (hinged) connection between the truss and the column • Rigid (fully restraint) connection between the truss and the column Left- Static scheme and rigidities (Ir, I -second moment area of the truss and of the column with constant cross section); Right- Transversal frames carrying crane girders ( Is, Ii - second moment areas of the top and bottom part of the columns) Models of the frame geometry for rigid connection between the column and the truss Effect of redundancy (rigid connection): a)- the column on the truss; b) the truss on the column; c) bending moment effects upon the chords of the truss Type of structure Ii/Is Ii1/Ii Is1/Ii Equal bays 7…10 10…30 1,5…3 Internal bays bigger than marginal bays 20…60 2.5…7 Ratio between the stiffness of the current columns of the transversal frames
- 4. Stiffnessoftheelementsofthetransversalframe The static computation follows the stages: a)-preliminary design of the cross section of the girder considered simply supported for determining the moment of inertia Ir; b)-preliminary design of the top and bottom part of the stanchion on the basis of a simplified scheme for determining the moments of inertia Is and Ii; c)-static computation of the frame for certain loads in order to determine the maximum sectional efforts.
- 5. STIFFNESSOFTHESTRUCTURALELEMENTSINTHETRANSVERSALFRAME The static computation follows the stages: a)-preliminary design of the cross section of the girder considered simply supported for determining the moment of inertia Ir; b)-preliminary design of the top and bottom part of the stanchion on the basis of a simplified scheme for determining the moments of inertia Is and Ii; c)-static computation of the frame for certain loads in order to determine the maximum sectional efforts.
- 6. LOADING SCHEMES ON THE TRANSVERSAL FRAME WITHOUT CRANE GIRDERS a)-the dead and live loads are always present; b)-only one alternative of each temporary loads presented on the schemes may taken once (for ex. snow on the left side or on the right side of the roof or on the whole roof, and so on); c)-the snow and the maximum temperature effects are not possible together; d)-the action of the force FT is always taken together with the action of the pair of forces R-r (or R-r); the action of the forces R-r may be taken without the action of the force FT; e)-if the seismic load is taken into account then neither the crab effects nor the wind are considered. RULES FOR COMBINATIONS
- 7. C.Teleman.StelStructuresIII. Lecture3 7 Fundamental group of actions: ik 1i i0Fk1FminFmaxFFd QQGsauGS iQ,11Q,1minG,1maxG,13 Accidental group of actions: ik 1i i2k11minmaxAd QQsauGGFS Rare combinations in limit state of serviceability: ik 1i i2k11minmaxAd QQsauGGFS Frequent combinations: ik 1i i0Fk1FminFmaxFFd QQGsauGS iQ,11Q,1minG,1maxG,13 Quasi-permanent combinations: ik 1i i2minmaxd QsauGGS Permanent and quasi-permanent actions a) dead loads transferred from the girder: 2 L qV H pp b) weight of the top (Gs) and bottom (Gi) of the column: ii ss h150G h100G Variable actions a) snow, transferred from the girder: ACTIONS,GROUPSOFACTIONSANDCOMBINATIONS 2 L qV H zz b) Reactions on the top of the column from wind on the roof, Vv, Hv and on the walls: c) maximum vertical (R) and horizontal reactions (RF) transferred by the runway system to the columns (determined with the influence lines): Timin Timax LqPr LqPR icF FR T ' v ' v Tvv Lpq Lpq
- 8. LOADINGSCHEMES(INTERNALFORCESANDMOMENTS)FORDESIGNOF THECOLUMN FORFRAMESWITHCRANEGIRDERS M N T N M Tcoresp corespmax max, , ; , , Reactions from crane girder on the columns Simplified schemes for the determinations of sectional efforts on columns Combinations of the sectional efforts for the design of the columns 1654 321 ;; ;;)( eRMePMePM ePMeGMeVVVM sii sssvzp e b b e b e t b e t bi s i s p s i p is 2 2 2 2 ; ; ;
- 9. 11 1 1 0 X P i 2 1 s 2 1 i 1P s 1P 11 P1 1 dsmndsm dsmMndsmM X 11P XmMM if XR II Stage. Correction of internal forces and moments 3 3 1 33 1 i 1 h EI3 11n n h EI3 r I Stage. Determine the unknown force or translation on the frame considering the joint is blocked: 0RRf Area moment method applied irR i f r R f 1 1111 R R r XrXX )dsmndsm( IE 1 dsm IE 1 dsm IE 1 ds IE m ds IE m i 2 1 s 2 1 s i 2 1 is 2 1 si i 2 1 s s 2 1 1 )dsmMdsmM( IE 1 dsmM IE 1 dsmM IE 1 ds IE mM ds IE mM i 1P s 1P s i 1P is 1P si i 1P s s 1P P Static computation of the frame with hinged joint between the column and the rafter
- 10. Reactions,bendingmomentsandstiffnesstohorizontaldisplacementsofcolumnswithvariablecross sectionandhingedconnectiontotherafter(fixedinfoundations) 31 2s 2 1 K; I I n; h h n 11n ; n 11n ; n 11n 4 4 3 3 2 2 2 23K1PX 1PXhM iA 2 2 0 i h KM3 X 0 iA MhXM 4i phK 4 3 X 2 ph XhM iA 3 3 1 ii 1 h EI3 RX 1;hRM iA n= 0.2 for cranes with small lifting capacity and heavy roofs; n= 0.08 for cranes with heavy lifting capacity and light roofs.
- 11. C.Teleman.StelStructuresIII. Lecture3 11 I. Sizing of the stiffness of the truss k depends on the slope of the top chord of the girder (k = 0.9 for p = 0% and k = 0.7 for p = 10%). I k I k A y A yx s s i i ( )2 2 Static computation of the frame with rigid joint between the column and the rafter 11 P1 1 P11ii r r 0rr Σr11 - the sum of the reactions at the top of the column when 1=1; Σr1P - the sum of the horizontal reactions at the top of the stanchions due to the external loads applied to the column. II. Area moment applied considering the rafter is infinitely rigid
- 12. DETERMINATIONOFTHEREDUNDANCYEFFECTS UPONTRUSSMEMBERS N N N N N N ik ik ik I ik ik ik I 0 0 ( ) ( ) max min minBikikik maxBikikik )T(qN )T(qN minmax/Bik ' B'k'iBik 0 ikik )T(/MMNN a. Hinged connection b. Rigid connection II Stage. Effect of the redundancy I Stage. Simply supported truss
- 13. 1 ,1 1 ik ik ik ik l N n E A 2 ,2 1 ik ik ik ik l N n E A ,2ikn ikN Knowing the values in the restrained joints 1 and 2 and the rotations of the supports for the simple supported truss under external loading the equilibrium equations may be written. 2 1 ,1 1 ik ik ik l n E A 2 2 ,2 1 ik ik ik l n E A ,1 ,1 1 ik ik ik ik l n n E A I. Rotations in the supports induced by unitary bending moments: II. Rotations on the supports induced by external actions : ,1ikn internal forces in the members ik when at the extremities 1 and 2 unitary bending moments are acting internal forces in the members ik undder external actions The stiffness of the members k1 and k2 and the coefficients of transmission in the static computation, k12 and k21 2 1 2 1 2 k 1 2 2 1 2 k 12 2 k 21 1 k c. Particular situation – uneven restraining conditions
- 14. Designoftheconnectionbetweenthecolumnandtherooftruss b,c 2 v 2 h 1 v 1 2 i max ih 11 NNNR n V N; n HT y y MN eVeHTM 0 1 1 M y2 shear 2 tech angle v p2 v t 2 h t2 0 h t 2 v 2 2 i max 2h 22 f 3 td N ; 4 d N 4 d N ; 4 d N n2 V N; n2 HT h2 h MN eVeHTM M1=(H+T)e +Ve2 M2=(H+T)e - Ve1 M1=(H+T)e