(X = 1.2 for D C ‘M ’), vd (= N J A J J is the norm alized design axial force with N c under the com bination considered, and V^h is obtained from equation (5.3) with yRd = 1.15.
2. A dequate vertical reinforcem ent of the column passing through the joint shall be provided so that
Av.i 28 2/3 4 V V (5-12)
N ote that equation (5.11) is w ritten in term s of equality of stresses. Equation (5.11) can be rew ritten in a simplified form as follows (in term s of equality of forces, not stresses):
^ 28 Vjh - v ch (5.13)
In equation (5.13), Vsh represents the contribution of the horizontal confinement reinforcem ent and Kh the contribution of the diagonal com pression struts.
A similar expression is also given by Cheung et al.
(1993).
5.4.4 Reinforcement
The minimum horizontal confinem ent reinforcem ent to be provided is 6 mm cp with a spacing the lesser of hJ2 or 150 mm. Additionally, at least one inter
m ediate vertical bar is provided betw een column corners on each side of the joint.
5.5 EC8 BEAM-COLUMN JOINTS, DUCTILITY CLASS ‘H’
5.5.1 Joint shear forces
The joint shear forces are determ ined as in section 5.4.1 but with yRd = 1.25.
5.5.2 Diagonal strut Procedure as in section 5.4.2.
5.5.3 Joint confinement
Procedure as in section 5.4.3, but in equation (5.11), yRd = 1.25 and the factor X = 1.0.
5.5.4 Reinforcement
The minimum horizontal confinem ent reinforcem ent to be provided is 6 mm cp with a spacing the lesser
of h j4 or 100 mm. If framing beams are on all four faces of the column, the spacing of the horizontal confinem ent hoops may be reduced to /zc/2, but not greater than 150 mm. A t least one interm ediate vertical bar is provided betw een column corners, but the maximum distance betw een consecutive bars is limited to 150 mm. The requirem ents for beam -colum n joint design are brought together in the following example.
Example 5.1: beam-column joint, DC ‘H’
As the design requirem ents for D C ‘L ’ are nom inal and those for D C ‘M ’ and D C TT are similar, this example will consider D C ‘FT only. The joint geom etry is shown in Figure 5.7 with 55 0 x 25 0 mm 2 beams framing into the four sides of the 40 0 x 40 0 mm column. The design data are as follows:
f ck =30 N/mm2 xRd = 0 .3 4 N /m m2 f yk =40 0 N/mm 2 q = 5 yRd = 1.25 For actions in the X direction:
A t + ^ s2 - 804 m m 2 (4 -1 6 c p )
A s3 + A s4 = 1610 m m 2 (8 -1 6 c p )
with Vc = 28 kN, F w = 34 kN and N c = 28 0 kN. Thus from equation (5 .3 )
^ j h “ YRd [ 2/3 C ^ s l + A s2) /y d ] “ V c
(note q/5 =1.0 )
= 1.25 x (2/3) x 80 4 x (4 0 0 /1 .1 5 ) x 10~3 - 28
= 233 - 28
= 205 kN From equation (5 .4 )
^ j v = y Rd [ 2/3 ( ^ S 3 + A d f y d ] + N J 2 - v w
= 1.25 X (2 / 3 ) x 1610 x (4 0 0 /1 .1 5 ) x 10-3 + 280/2 - 34
= 467 + 140 - 34
= 573 kN
For actions in the Y direction:
A s| + A s2 — 1610 m m 2 ( 8 —16cp)
A s3 + A s4 - 2 5 1 0 m m 2 (8 -2 0 c p )
Figure 5.7 Exam ple 5.1: details of the sizes of the m em bers for a beam -colum n joint designed to D C ‘H \
SUMMARY 85 with Vc = 18 kN, Kw = 16 kN and N c = 480 kN. Thus,
as actions in the X direction
Kjh = 1.25 x (2/3) x 1610 x (400/1.15) x 10~3 - 18
= 467 - 18
= 449 kN
Vjv - 1.25 x (2/3) x 2510 x (400/1.15) x 10 3 + 480/2 - 16
= 728 + 240 - 16
= 952 kN
In EC8 there is an approxim ation to Vjv as I'., = V ^ K I h c).
The values of are checked against the integrity of the diagonal strut (equation (5.5), that is
Vfr ^ 20TRd6j/zc (interior joint)
Thus b-} = bc = 400, xRd = 0.34 N/m m2 (fck = 30 N/mm2), hc = 400 and b ■ is the lesser of
bc = 400 mm or
bw + hJ2 = 250 + 400/2 = 450 mm Thus b} - bc = 400 mm and
Fjh = 20 x 0.34 x 400 x 400 x 10-3
= 1088 > 852 kN
Thus the diagonal strut integrity requirem ent is met.
The required horizontal reinforcem ent is obtained from equation (5.12) with the factor 1.2 om itted.
The com ponents of equation (5.12) are evaluated below for direction Y with (Asl + A s2) = 1610 m m 2, Vc = 18 kN, b} = 400 mm and h]C = 300 (say) and /ijw = 450 (say):
[ K YRd < A l + A l ) f y d - K V b f ac
= [% x 1.25 x 1610 X (400/1.15) - 18 x 103]/400 x 300
= (466 666 - 18 000)/400 x 300
= 3.74 N/mm2 Ed = N J A J cd
= 480 x 103/[4002 x (30/1.5)]
= 0.15 N/mm2
Thus
[xRd (12 xRd + vd / cd)]1/2
- [0.34 (12 x 0.34 + 0.15 x 2 0 ) p
= 1.55 N/mm2 H ence
A h f yJ bi *jw = 3-74 - L55 = 2-15 N/mm 2 Thus
A sh = 2.19 x 400 x 450/(400/1.15) = 1133 m m 2 and
A SV1 = 1133 x 300/450 x 2/3 = 503 mm 2
The values of A sh and A svi above must be at least equal to the minimum requirem ents for D C ‘H ’; see section 5.5.4. Finally, it is necessary to check that the limiting value of crct = / ctm/yc is not exceeded.
From Table 1.6, / ctm = 2.9 N/m m 2 and thus a ct = 2.9/1.5 = 1.93 N/m m2. From equation (5.7)
xh = (1.25 x 2/3 x 1610 x 400/1.15 - 18 x 103)/400 x 300 = 3.74 N/m m2 From equation (5.8)
a v = [(480 x 103/2) + 503 x 1.5
x (400/1.15)]/400 x 300 = 4.19 N/m m 2 a h = 1133 x (400/1.15)/400 x 450 = 2.18 N/mm 2 Thus crct is given by
CTct = (-4.19 - 2.18)/2 ±
{[(-2.18 + 4.19)/2]2 + 3.742}1/2
= - 3.19 ± 3.87 N/m m2
A positive sign denotes tension and thus a ct = - 3.19 + 3.87 = 0.68 < 1.93 N/mm 2. Thus the upper limit of 1.93 N/mm2 is not exceeded.
5.6 SUMMARY
N ote that in the 1993 draft of EC8 the requirem ent that o-ct(max) ^ /ctm/Yc is satisfied if equations (5.11) and (5.12) are complied with. The principles of joint design set out in EC8 are in line with the proce
dures reported by Cheung et al. (1993) and are
intended to minimize joint dam age in a m ajor ea rth quake. D am aged joints will cause a substantial reduction in the am ount of energy that can be dissi
pated by the framing elem ents and they are virtu
ally impossible to repair. The design of seismic joints necessitates stringent detailing requirem ents, and current guidelines may be obtained from A C I (1991) and Cheung et al. (1992) Typical details are given in A ppendix H.
REFERENCES
A C I (1991) Design o f B eam -C olum n Joints fo r Seismic Resistance, A C I SP-123.
Cheung P.C., Paulay T. and Park R. (1993) B ehaviour of beam -colum n joints in seismically loaded reinforced concrete frames, /. Inst. Struct. Eng., 71, No. 8 (20 April)
N C E (1993) Finding fault, New Civil Eng., 21 May.
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