Материал: Scientific Herald of the Voronezh State University of Architecture and Civil Engineering
Issue № 1(29), 2016 ISSN 2075-0811
2.4. Bending resistance of the joints considering the tensile strength [8]:
MN ,Rd M pl,Rd ,b |
1 Nsd / Nb, pl |
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(9) |
1 0,5(A 2btf ) / A |
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where Mpl, Rd. b is a plastic moment of the support slab of the column: |
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Mpl,Rd,b Wb fyep / Mo ; |
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Wb is an inertia moment of the support slab of the column; γМо = 1,1; fyер is the bending resistance of the support slab material; A is the area of the transverse section of the column; Nb, pl is a calculation longitudinal strength of the column base: Nb, pl = Afy / γMo; fy is the compressive resistance of the support slab material; tf is the thickness of the cap of the column section.
2.5. Determining the rigidity of the compressed concrete [7]:
Kc Ec |
leff ,cpbeff ,c |
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1, 275 |
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where Ec is the elasticity modulus of concrete foundations;
leff ,ср tf 2,5tep.
2.6. Determining the rigidity of a bended support slab [7, 8]: –– without considering extra forces:
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epb |
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–– considering extra forces: |
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epb |
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where Eep is the elasticity modulus of a steel support slab.
2.7. Determining the rigidity of the tensile bolts [7]: –– without considering extra forces:
Kb Eb 2Ab ;
Lbef
–– without extra forces:
Kb Eb 1,6Ab ,
Lbef
where Ab is the area of the longitudinal section of bolts.
(11)
(12)
(13)
(14)
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Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture
The equivalence rigidity of the i-th row of bolts [6, 7]:
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Kepb,i |
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2.8. Determining vertical shears of the connections (Fig. 6.) [6, 9]:
t,l MSd NSd zc,r ;
zKt,l
MSd NSd zt,l .
c,r zKc,r
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(16)
(17)
(18)
Fig. 6. Mechanical model of the joint:
а) at different signs of efforts in the connections (detachment of the slab from the foundation); b) at identical ones (compressed ones)
2.9. Determining the rotational angle of the support slab (Fig. 6а) [9]:
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c,r |
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MSd NSd zt,l |
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MSd NSd zc,r |
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2.10. Determining the rotational resistance [5, 9]: –– at a small eccentricity e < zc, r:
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Issue № 1(29), 2016 |
ISSN 2075-0811 |
–– at a large eccentricity e > zc, r:
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Kt,l |
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Kc,r |
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where Kc, l and Kc, r are the rigidities of the components under tension and shear; μ is the coefficient considering a reduction in the rigidity of a plastic range providing that a bending moment is 2/3 larger than the bending of the components:
1,5 M Sd 2,7 ;
M Rd
e0 Kc zc,r Kt zt,l .
Kc Kt
3. Sample calculation. The base of the column is to be computed: the thickness of the support slab is tep = 28 mm, thickness and width of a section of the column tf = 10 mm, bf = 200 mm, twc = 6 mm, hwc = 380 mm; bolts Ab = 560 mm2, fub = 192 N/mm2, FSd = 95 kN; MSd = 170 kN·m; the height of the plate of the concrete foundation h = 1200 mm (Fig. 7).
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Fig. 7. Distribution of bolts in the column base: а) a cut; b) a plan
The results of the calculation are specified in Table.
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Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture
Table
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Calculation data |
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Tensile resistance of the joints of the |
F1,t,Rd |
min Ft,Rd ,1; |
Ft,Rd ,3 min 230750; 193536 |
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first row of bolts |
193,5 kN FSd |
95 kN |
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Tensile resistance of the joints of the |
F2,t,Rd |
min Ft,Rd ,1; |
Ft,Rd ,3; Fbwt,Rd |
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second row of bolts |
min 319555; 337882; |
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193536 193,5 |
kN FSd 95 kN |
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Bending resistance of the column base |
M Rd Ft,Rd |
rb Aeff |
f j rc |
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181,6 kN m MSd |
170 kN m |
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Bending resistance of the joint consi- |
M N ,Rd |
M pl,Rd ,b |
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1 Nsd / Nb, pl |
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1 0,5(A 2bt f ) / A |
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dering the tensile force |
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173,7 kN m MSd |
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170 kN m |
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MSd NSd zc,r |
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0, 46 mm ; |
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t,l |
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zKt,l |
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Displacements of the support slab |
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MSd NSd zt,l |
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c,r |
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0,13 mm |
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zKc,r |
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Rotational angle of the support slab |
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t,l |
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c,r |
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0,46 0,13 1,36 10 3 |
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434,12 |
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z2 |
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Nmm / radian |
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1,95 10 |
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Rotational resistance |
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e0 |
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Kt,l |
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Kc,r |
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Conclusions
1.A method of the evaluation of the rigidity and strength of joints of metal columns with foundations under the effect of a bending moment and axial vertical force considering the rigidity and strength of members of a joint.
2.A degree of accuracy of calculations using the component method in compliance with the Eurocode 3.
3.The previously suggested [6] method of predicting the operation of members of a joint due to more accurate determination of the sizes and shapes of elastic and plastic compressive zones depending on the models suggested in [5, 6, 9].
References
1.Evrokod-2 (TKP EN 1992). Proektirovanie zhelezobetonnyx konstrukcij. — CEN Bryussel', 2004.
2.Evrokod-3 (TKP EN 1993-1-8). Proektirovanie stal'nyx konstrukcij. Ch. 1—8. — CEN Bryussel', 2005.
3.Ledenyov, V. V. Raschet boltovyx soedinenij s uchetom dopolnitel'nyx sil / V. V. Ledenyov, T'yu Txi Xoang An' // Stroitel'naya mexanika i konstrukcii. — 2013. — № 2 (7). — S. 80—85.
4.SNiP 53-100-2010. Stal'nye konstrukcii / Gosstroj Rossii. — M.: GUP CPP, 2010. — 225 s.
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Issue № 1(29), 2016 |
ISSN 2075-0811 |
5.James, A. S. Ultimate Strength Prying Models for Bolted T-stub Connections / A. S. James // Engineering Journal, American Institute of Steel Construction. — 2002. — № 3. — P. 136—147.
6.Kestutis, U. Component Method Extension to Steel Beam-to-Beam and Beam-to-Column Knee Joints under Bending and Axial Strengths / Kestutis Urbonas, Alfonsas Daniūnas // Journal of Civil Engineering and Management. — 2005. — № 11 (3). — P. 217—224.
7.Latour, M. Column-Base Plate Joints under Monotonic Loads: Theoretical and Experimental Analysis / Massimo Latour, Vincenzo Piluso, Gianvittorio Rizzano // 7th International Workshop on Connections in Steel Structures. — Timisoara, 2012. — 12 pp.
8.Thornton, W. A. Prying Action — a General Treatment / W. A. Thornton // Engineering Journal, American Institute of Steel Construction. — 1985. — Vol. 22, № . 2. — P. 67—75.
9.Wald, F. Component Method for Steel Column Bases / F. Wald, Z. Sokol, C. M. Steenhuis // Heron — Steel Column Bases. — 2008. — Vol. 53, № 1 (2). — 20 pp.
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