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A beam-to-column connection with bolted through diaphragms shown in figure 8.6 is to be checked if the connection details are appropriate to allow for the desired failure modes under the influence of a strong earthquake. The column is the hot-finished square hollow section 400 x 400 x 16 of Grade EN-10210 S275J2H. The beam is the hot-rolled I-section 500 x 200 x 10 x 16 of Grade JIS G3136 SN400B. The plate materials are also of the same grade of steel. The high-strength bolts used are of Grade 10.9 with a nominal diameter of 20 mm. The nominal values of the yield and ultimate tensile strengths for each material are shown below:
The ratio of the fully-plastic moment of the column to that of the beam is computed at 2.1, which shows that this beam-to-column assembly satisfies the strong column weak beam condition.
The beam centre-to-centre span is 8000 mm. Assume the inflection point at the centre of the span and check if a plastic hinge can form at sections adjacent to the beam splice.
Assume that a shear force of 63 kN due to gravity loads acts on the connection.
Moment demand at column face
The flexural capacity of the beam at the net section at the last row of bolts can be calcu-lated by equation 8.9. Namely,
Mb,n* = [(200 - 22) · 16 · (500 - 16) · 400 + (500 - 2 · 16 - x) · x · 10 · 235]10-6= 672 kNm
where
x = - 22 · = 174 mm
The ratio of the net section flexural capacity to the beam fully-plastic moment is:
= = 1.34
which is a sufficiently large number to warrant formation of a plastic hinge in the beam. The required moment demand at the column face is given by equation 8.11 as:
Mcf= · 672 = 741 kNm
Flexural capacity of stub beam
Equation 8.12 gives the flexural capacity, at the column face, of the stub beam section
Material Yield strength
(N/mm2)
Ultimate tensile strength (N/mm2)
Square hollow section 275 410
235 400
900 1000
I-section and plates High-strength bolts
500 - 2· 16 2
672 2130· 235 · 10-6
3800 3800 - 355 Mb,n*
Wplfb,y
16· 400 10· 235
Mj,cf* = · 1012 = 1031 kNm
where sc = 70 mm. The flexural capacity of 1012 kNm was calculated by equation 8.9 as:
Mb,n* = [(340 - 2 · 22) · 16 · (500 - 16) · 400 + (500 - 2 · 16 - x) · x · 10 · 235]10-6
= 1012 kNm where
x = - 2 · 22 · = 114 mm
If the net section failure through the first bolt holes accompanies shear ruptures of the beam web (see figure 8.6), equation 8.13 gives the flexural capacity of the beam flanges while equation 8.14 gives the flexural capacity of welded web joints to the column flange and to the diaphragms. Namely,
Mb,f,u= [(340 - 4 · 22) · 16 · (500 - 16) · 400] · 10-6= 781 kNm
Mb,w,u= 0.897 · 235 + · 10-6
= 191 kNm
where Le = 70 mm. The value of m of 0.897 used in the above equation was calculated by equation 8.5 as
m = 4 · = 0.897
The moment capacity at the column face is equal to the sum of Mb,f,uand Mb,w,u calcu-lated above (see also equation 8.1). Namely,
Mj,cf* = Mb,f,u+ Mb,w,u= 972 kNm
The above calculations show that the latter failure mode is more critical than the former failure mode. However, even with the latter failure mode the flexural capacity of the stub beam becomes much greater than the moment demand of 741 kNm. This is due to hori-zontal haunches prepared on the stub beam side to accommodate 6 bolts.
Design of beam splice
Details and dimensions of the beam splice are largely governed by fabrication require-ments. The cross-sectional areas of the splice plates are significantly greater than those of the beam flanges and webs. There is no need to check the net section strength of the splice plates in this example. The following calculations of bolted joints are based on
3800
The shear resistance of high strength bolts per shear plane is given as
Vb* = = 10-3= 151kN
Shear planes are assumed to pass through unthreaded portion of the bolts. All the bolts are used as double shear joints and therefore the shear resistance of each bolt is equal to 2Vb*.
The bearing resistance of a bolt Bb* is determined by the thinnest plate on which the bolt bears. Either the beam flange with the thickness of 16 mm or the beam web with the thick-ness of 10 mm governs the bearing resistance at a bolt hole. The bearing resistance is a function also of the end distance, bolt spacing, bolt diameter and bolt hole diameter. The values of the bearing resistance calculated by using the bearing resistance equation in table 6.5.3 of Eurocode 3 are as follows:
The partial safety factor
M0was taken to be unity, because bolt hole elongation is one of the preferred failure modes. Thus, the design shear resistance of each bolt is always gov-erned by the design bearing resistance Bb*.The flexural capacity of the beam splice can be calculated as the sum of the flexural capacity of the beam flange-to-splice plate joint with 6 bolts and that of the beam web-to-splice plate joint with 2 bolts. Namely,
Mbs* = [(2 · 242 + 4 · 211) · (500 - 16) + 2 · 152 · 240] · 10-6= 716 kNm
Note that only the two bolts closest to the top flange and those closest to the bottom flange are assumed to carry flexural loads. The flexural capacity of the beam splice at the column face is (see equation 8.11 and figure 8.6):
Mbs,cf* = 716 · = 751 kNm
which is greater than the moment demand of 741 kNm. The value of 180 mm in the above equation stands for the distance from the column face to the section at which bending and shear loads are carried only by the beam splice.
The shear load is resisted by the two bolts at the centre. The shear capacity of the beam splice is given as:
while the required shear capacity Vbsis the sum of the shear loads due to gravity and earthquake loads. Namely,
Vbs= 63 + = 258 kN
A block shear failure mode is possible on the splice plates with the total thickness of 12 + 9 mm as shown in figure 8.6. The shaded portions in figure 8.6 may tear out. According to Eurocode 3 Clause 6.5.2.2, the design resistances to block shear become 1599 kN and 1565 kN for the block shears 1 and 2, respectively. The partial safety factor M0was taken to be unity, because shear and tensile ruptures are preferred failure modes. The block shear resistances are slightly greater than the bearing resistances of 6 bolts in the flange, which are equal to 2 · 242 + 4 · 211 = 1358 kN. Thus, the block shear failure is less critical.
The above calculations suggest that, in the beam-column assembly adopted in this exam-ple, a plastic hinge forms in the beam section adjacent to the beam splice accompanying local buckling of the beam flanges and webs. The next critical section is the net section through the last bolt holes away from the column within the beam span. Some bolt hole elongation can be anticipated. However, note that the ultimate strength equations for the bolt hole bearing and block shear specified in Eurocode 3 are more conservative than sim-ilar equations recommended in other codes like the AISC LRFD Specification (1999).
A beam-column assembly with details similar to this example was recently tested. The assembly showed an excellent plastic rotation capacity sustaining local buckling in the beam flanges and web at sections just outside the beam splice (Kurobane 2002). The beam flange necking due to tensile yielding was observed at the section of the last bolts.
These failure modes were close to those anticipated at the design stage.