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Fc, r, Rd

Scientific Herald of t he Voronezh State University o f Architecture and Civil Engineering. Construction and Architecture

а)

b)

Fig. 2. Strengths applied to a support sla b:

а) two r ows of anchor bolts are stretched, the slab is compressed under the right cap; b) support slab is compressed under both c aps;

Ft, l, Rd is a tensile loa on the left part of the sup port slab;

is a compressive str ength on the right part of the support sla ;

 

Fc, l, Rd is a co mpressive strength on the left part of th

support slab;

 

MSd is bending mo ment; NSd is a longitudinal strength;

zc, l is an arm of the left compressive strength; zc, r is a n arm of the

ight compressive strength;

 

zt, l is an arm of the right tensile strength; z is

n arm

( distance betw een the centres of the stretched and compressed zone s)

 

c)

d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 2 (end). Strength applied to the support slab:

c)a r ow of anchor bolts is stretc hed, the slab is compressed under the right cap;

d)the same as “b” but the tension areas of the slab reach the edges

96

Issue № 1(29), 2016

ISSN 2075-0811

а)

 

ep

ep

x

 

x

 

e)

 

 

ep

 

ep

x

 

 

ep

b)

f)

c)

g)

d)

h)

Fig. 3. Scheme of the failure of the support slab:

а, h) plastic areas are joined together; b) plastic areas reaches the transverse and longitudinal sides of the support slab;

c, g) the same for the transverse one; d) round plastic zones; e) angular plastic zones; f) rectangular plastic zones

2. Solution of the problem

2.1. Determining the compressive resistance of the joints as a minimum of the function [5, 7]:

 

 

 

Ft,Rd min FRd ,1, FRd ,2 , FRd ,3 .

 

(1)

Considering extra forces at

 

 

 

 

 

 

 

 

 

 

 

 

tp 2,07m 3

Ab

 

tep :

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Lbef leff

 

 

 

 

 

 

 

 

(2)

 

(8n 2d)M

 

 

2M

 

n

F

 

 

 

 

 

 

pl,1,Rd

 

pl,2,Rd

 

 

Ft,Rd min

 

 

 

 

;

 

 

t,Rd

;

Ft,Rd ,b

;

 

 

 

 

 

 

 

 

 

 

2mn d (m n)

 

m n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture

without considering extra forces at

tp 2,07m3

Ab

tep :

 

Lbef leff

(3)

 

 

 

 

 

2M

 

 

 

pl,1,Rd

 

Ft,Rd min

 

 

; Ft,Rd ,b

,

 

 

 

 

m

 

 

 

where m is the distance between plastic hinges and the axis of the bolt (for a welded column m ec 0,8ac 2 , ac is the height of the leg of the weld; ec is the distance between the axes of the compressed bolts to the column cap; for a rolled beam m ec 0,8r , n is the distance be-

tween the extra strength Q and axes of the bolts ≤1,25m); d is the diameter of the plate; Lbef is the effective length of anchor bolts:

Lbef 8db tg tep tn / 2,

where db is the diameter of anchor bolts; tg is the thickness of the base between the support slab and the upper one with the foundation base; tn is the thickness of the plate; Mpl,1, Rd, Mpl,2, Rd are plastic bending moments of the support slab corresponding to the first and second failure mechanisms:

 

l

t2

f

y,ep

 

M pl,Rd

eff

ep

 

,

 

 

 

 

 

 

4 Mo

where leff is the effective length of the compressed zone of the support slab:

leff min 4m 1, 25ex ; 4 m; 0,5b; 2m 0,625ex 0,5w;2m 0,625ex eep ; 2 m 4eep ; 2 m w ;

tep is the thickness of the support slab; fy, ер is the bending resistance of the support slab material;

γМо is the coefficient: γМо = 1; w is the distance between two axes of bolts; b is the thickness of the support slab; ex, eep are geometrical characteristics (Fig. 3, 4); Ft, Rd, b is a calculated compressive resistance of anchor bolts:

FRd ,3

Ft,Rd ,b , Ft,Rd ,b

0,9As fub

;

(4)

 

 

 

Mb

 

As is the area of the longitudinal section of tensile bolts; fub is the tensile resistance of bolts; γМb = 1,1 is the coefficient.

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Issue № 1(29), 2016

 

 

ISSN 2075-0811

а)

 

ep

 

ep

 

 

 

 

c

c

ep

 

c

c

 

 

 

 

 

b)

 

ep

 

ep

 

 

 

 

c

c

 

c

 

c

ep

a

 

 

 

 

 

 

x

2

 

 

c

 

 

Fig. 4. Denotation of the sizes used in the calculation of the column: а) of a rolled section; b) of a welded section

2.2. Compressive resistance of the joints [1, 7]:

 

 

Mc,Rd

 

 

 

 

 

 

 

 

Fс,Rd

min f jbeff leff ,c ;

 

 

,

(5)

 

 

 

hc tcf

 

 

 

 

 

 

 

 

where fj is the compressive resistance of concrete under concentrated axial loads determined according to the European Standard [1]:

f j

2k j fck

; k j

a b

,

 

1 1

3 c

ab

 

 

 

where fck is the compressive resistance of concrete; a, b is the width and length of the support slab (Fig. 5);

a1 min a 2ar ; 5a; a h; 5b1

b1 min a 2br ; 5b; b h; 5a1

h is the height of a concrete base plate; γс = 1,5; beff, с, leff, с the compressed zone of T-shaped section:

иa1 a;

иb1 b;

is the effective width and length of

A

 

Fsd Ft ,Rd ,b

, b

 

Aeff ,c

, l

b 2c ,

 

 

eff ,c

 

 

eff ,c

 

b 2c

eff ,c

 

 

 

f j

 

 

 

99

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture

bc, c are the sizes specified according to Fig.5; Mc, Rd is a plastic moment in the column considering the shear and axial strengths (according to the European Standard [2]):

at e = Msd/Nsd > zc, r:

Mc,Rd min Ft,l,Rd z NSd zc,r ; Ft,l,Rd z NSd zt,l ;

(6)

at e = Msd/Nsd < zc, r:

 

Mc,Rd min Fc,l,Rd z NSd zc,r ; Fc,r,Rd z NSd zc,l .

(7)

а)

 

1

r

r

 

r

 

1

b)

 

 

c

 

c

 

 

c

eff

 

 

c

b

b

c

 

 

Fig. 5. Sizes of the column base:

а) position of the column on the support slab; b) position of the effective compressed zone on the support slab

2.3. Bending resistance of the column base [1, 7]:

MRd Ft,Rd rb Aeff f j rc ,

(8)

where rb is the distance between the axes of the tensile bolts to the neutral line:

 

r

hc e ;

 

b

2

c

 

 

 

 

rc is the distance between the centre of the compressed zone to the neutral line:

rc h2c c b2eff .

100

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