Analysis On Shear Behavior of High-Strength Bolts Connection
Analysis On Shear Behavior of High-Strength Bolts Connection
Analysis On Shear Behavior of High-Strength Bolts Connection
www.springer.com/journal/13296
Abstract
Because of high cost of tests and numerical calculation using solid element of high-strength bolts connection in steel
frameworks, it is important to find an accurate and simplified approach to describe the shear behavior of high-strength bolts
connection. The paper aims to find a spring element to simulate the shear behavior instead of solid element in structure. Firstly,
solid element model of high-strength bolt connection is established, which is proved correct and applicable comparing with
existing typical shear tests. Then, base on the reliability of finite element model, the shear behavior of bolts connection is further
discussed through a large number of parameter analyses. The three feature points and four stages of the simplified shear model
are calibrated according to tests and calculation results. A simplified shear behavior model and hysteretic criterion of high-
strength bolts connection are proposed. According to cases study, feasibility of the proposed model is validated. The proposed
model gives a simple process to provide quite accurate results, which provides a great tool for engineering applications.
Keywords: high-strength bolts connection, finite element method (FEM), shear behavior, hysteretic criterion, feature points
Table 1(b). Specimens parameters of Chen et al. (2004) (mm) Figure 5. Test results of Chen et al. (2004).
core core cover Bolt
Bolts
Specimen plate plate plate spacing µ Monotonic displacement loading was applied until the
level D tp×tp lp lc×tc e1 e2 relative displacement of the core and cover plates was
HBS1 10.9 16 200×16 265 165×12 80 90 0.212 more than 4~5 mm. Deformation of specimens are shown
HBS2 10.9 24 300×20 315 215×12 100 140 0.265 in Fig. 5 (a). Comparative analysis of load-deformation
curves between tests and finite element model are shown
206 Yongjiu Shi et al. / International Journal of Steel Structures, 11(2), 203-213, 2011
in Fig. 5 (b) and (c). From the figures, it can be seen that
nonlinear finite element analysis is reliable to simulate
the load-displacement curves of specimens in this paper.
Although there are some deviations in early stage of
confined stage, the simulation of shear carrying capacity
is accurate. The carrying capacity is the greatest concern
in this paper. The main reason of deviations is that
constitutive relationship used in paper is simplified linear
model, which is different from real steel constitutive
relationship.
core core cover Bolt failure. Specimens deformations are shown in Fig. 7 (a)
Bolts
Specimen plate plate plate spacing µ and comparative analysis of load-deformation curves are
level D tp×tp lp lc×tc e1 e2 shown in Fig. 7 (b). From the figures, finite element
S1 10.9 20 80×16 255 155×8 40 65 0.242 analysis and experimental results are in good agreement.
model is proposed to characterize the shear mechanical between holes (Fig. 9 (a)). The carrying capacity of this
properties of the high-strength bolts connection. This situation can be defined by equation (2):
assumption tends to be safer. The aim of the analysis
b b
below is to obtain the calculation method of these stages Nc1 = d∑tfcu (2)
and feature points.
Because the high-strength bolts connection has to
4.1.1. Friction stage (stage OA) overcome friction first, the ultimate carrying capacity of
In this stage, shear is transmitted by the friction of this failure mode is the sum of equation (1) and (2), such
contact surfaces. The relative displacement between the as equation (3):
core plate and cover plate is quite small. Friction force is
b b b b
calculated according to equation (1) (GB50017-2003, Nc = Nm + Nc1 = d∑tfcu + nfµPt (3)
2003).
(b) Bolts screw shear failure
b
Nm = nfµPt (1) When the bolt diameter is small but the connected steel
plates are thick, failure mode of bolts screw shear failure
In which, when it is a single shear model (one cover may occur (Fig. 9 (b)). If the bolts can be defined as the
plate), nf is 1 while when it is a double shear model (two ideal elastic-plastic material, the capacity of this mode is
cover plates), nf is 2. calculated by following equation (4):
b 1-n (πd2 ⁄ 4)fb
Nv = -----
4.1.2. Slip stage (stage AB) f y (4)
When the external force exceeds the friction of contact 3
surfaces, the curve goes to point “A” and the contact If this failure mode occurs, bolts screws have undertaken
surfaces have a relative “slip”. The relative displacement in deep plastic status with large deformation. Pre-tension
between core plate and cover plate is significantly loss seriously and the contribution of friction on bearing
increased while the load changes little. Slip displacement capacity will not be taken into account.
is mainly caused by the gap of the holes wall and the bolt
screw changing and the hole itself deformation. (c) Plate fracture failure
When the plates have more openings or the openings
4.1.3. Confined stage (stage BC) are closer to the edge of the plate whose net section are
In this stage, the bolt screws are in contact with the weaken seriously, the plate fracture failure may occur
holes walls of the core plate and cover plate. The external along the net section of component (Fig. 9 (c)). If the
force is transmitted by confined process of bolt screws steel can be defined as the ideal elastic-plastic material,
and holes walls. Inflection points occur several times in the carrying capacity is as follows equation (5):
stage B-C, which is mainly caused by the different failure
b
modes of the connection. When confined stage starts, the Nf = An fy (5)
high-strength bolts connection properties are similar to
the ordinary ones’ which have three failure modes In this failure mode, the whole cross-section of plates
(GB50017-2003, 2003): (a) plates crushing failure; (b) yield with a large plastic deformation, which makes the
bolts screw shear failure; (c) plates fracture failure plates thinner and pre-tension loss seriously without
(shown in Fig. 9). considering the contribution of friction on bearing capacity.
Therefore, shear capacity of the high-strength bolt
(a) Plates crushing failure connection is determined by the minimum value of
When the bolt diameter is large but the connected steel equations (3), (4), (5), such as equations (6):
plates are thin, a great compressive stress and plastic
b b b b
deformation will occur in bolt holes walls. Local pressure Nv, min = min(Nc , Nv , Nf ) (6)
or extrusion caused by bolt screw eventually results in
bolt hole being elongated and steel plate being fractured 4.1.4. Extreme stage (stage CD)
In practice, it means the component loss the capacity
and is defined as failure after the point C. It is not like
finite element method which will continue to calculate, so
the stage C-D is not the problem to concern in this paper.
Table 3. Specimens parameters of S1~S6 series strength bolts connection in parameter analysis, bp=lc=
Bolts
120 mm is used and the diameter of bolt hole is 2.0 mm
Series fy tp tc Failure larger than the bolt screw. Constitutive models of bolt and
D P (MPa) (mm) (mm) µ
Name level mode steel are both ideal elastic-plastic constitutive model.
(mm) (kN)
The main parameters include the friction coefficient µ,
10.9 M16 110 270 16 8 0.3 A bolt pre-tension value Pt, high-strength bolts strength
10.9 M20 155 270 16 8 0.3 A level (10.9 or 8.8), bolt diameter d, core plate thickness tp,
S1 10.9 M22 190 270 16 8 0.3 A cover plate thickness tc and steel yield fy.
10.9 M24 225 270 16 8 0.3 A Equation (6) is used to determine the failure modes:
10.9 M27 290 270 16 8 0.3 A “A” stands for plates crushing failure; “B” stands for
10.9 M20 155 270 24 12 0.3 A bolts screw shear failure; “C” stands for plates fracture
10.9 M22 190 270 24 12 0.3 A failure (Table 3).
S2 The results of the parameters analysis are as follows
10.9 M24 225 270 24 12 0.3 A
(Fig. 10).
10.9 M27 290 270 24 12 0.3 A
10.9 M20 155 270 14 7 0.3 A 4.2.1. Method for determining point A
10.9 M20 155 270 16 8 0.3 A O-A stage is friction stage when little deformation of
10.9 M20 155 270 18 9 0.3 A components occurs and plates and bolts have not
S3 10.9 M20 155 270 20 10 0.3 A contacted. So, point A is only possibly related with
10.9 M20 155 270 22 11 0.3 A friction coefficient µ and pre-tension Pt. S1 and S5 series
10.9 M20 155 270 24 12 0.3 A are selected to calculate.
10.9 M20 155 270 26 13 0.3 A
10.9 M20 155 270 16 12 0.3 A (1) Determine Ax
10.9 M20 155 270 18 12 0.3 A The results of S1 and S5 series are shown in Fig. 9 (a),
S4 10.9 M20 155 270 20 12 0.3 A (b). It can be seen that Ax is basically stable at 0.06mm
10.9 M20 155 270 22 12 0.3 A
and is independent of the friction coefficient and pre-
tension value. So the value of Ax for simplified model is
10.9 M20 155 270 24 12 0.3 A
proposed as 0.06 mm.
10.9 M20 155 270 24 12 0.2 A
10.9 M20 155 270 24 12 0.3 A (2) Determine Ay
S5 10.9 M20 155 270 24 12 0.4 A The results of S1 and S5 series for Ay are shown in Fig.
10.9 M20 155 270 24 12 0.5 B 10 (c), (d). The results are equal to the friction calculated
10.9 M20 155 270 24 12 0.6 B by equation (1), so Ay can be determined according to
10.9 M20 155 270 24 12 0.3 A equation (1).
S6 10.9 M20 155 400 24 12 0.3 B
8.8 M20 110 400 24 12 0.3 B 4.2.2. Method for determining point B
A-B stage is slip stage when the relative displacement
between core plate and cover plate is significantly increased
strength bolts connection. The whole process of the shear while the load changes little. Bolts screw contact with
curve (Fig. 8) is expected to obtain. The displacement core plate and cover plate in order and point B is related
loading is applied and the maximum displacement is applied with friction coefficient µ, pre-tension Pt, bolt diameter d,
to 10 mm which is enough to make the component failure. core plate thickness tp and cover plate thickness tc. So
Six series (Table 3) of specimens are selected for S1~S5 series are selected to calculate.
parameter analyses for the feature points, then the specific
expression of the feature points can be summarized. S1 (1) Determine Bx
series focus on the impact of bolt diameter on the shear The results of S1~S5 series are shown in Fig. 10 (e)~
behavior in the case of thin core plate; S2 series focus on (g). It can be seen that Bx is basically stable at 1.85 mm
the effect of bolt diameter in the case of common and is independent of the friction coefficient, pre-tension
thickness core plate; S3 series focus on the impact of value, core and cover plate thickness. So for the case that
different thickness of core plate and cover plate; S4 series the hole diameter is 2 mm larger than the screw diameter,
focus on the impact of different thickness of core plate in a value of 1.85 mm is suggested for Bx, which means Bx
case of cover plate with the same thickness; S5 series is 0.925 times of difference between the hole and the
focus on the impact of different friction coefficient; S6 screw. On one hand, this little difference is mainly caused
series focus on the impact of different yield strength of by the micro-tensile deformation, which leads screw
bolts and steel. holes not circular but slightly elliptical and makes the
In order to satisfy the structure requirements of high- screw contact with holes walls earlier. On the other hand,
Analysis on Shear Behavior of High-Strength Bolts Connection 209
it is also caused by the friction between the bolt nut and 4.2.3. Method for determining point C
the cover plate. Bx can also be determined as the same as B-C stage is confined stage when the bolt screws have
the difference between the hole and the screw for more already been in contact with the core plate and cover
security considerations. plate. The external force is transmitted by the confined
process of bolts screws and holes walls. Bolts and plates
(2) Determine By are likely to enter yield status at this time, so point C is
As A-B is slip stage and load is essentially constant, related with friction coefficient µ, pre-tension Pt, bolt
By=Ay is proposed in the model and the method to level, bolt diameter δ, core plate thickness tp, cover plate
determine By is in the same way as Ay. thickness tc, steel and bolt yield strength and failure
210 Yongjiu Shi et al. / International Journal of Steel Structures, 11(2), 203-213, 2011
b
bolts connection established in this paper are in good Nc1 : part of the shear capacity under plate crushing
agreement with typical test results. The elements types, failure mode
b
bolts force behavior, the material constitutive relationship Nc shear capacity under plate crushing failure
and contact are proved reliable. mode
b
(2) Based on the accuracy of the finite element model, Nv : shear capacity under bolt screw shear failure
the three feature points and four stages of shear behavior mode
b
simplified model of high-strength bolt connection are Nf : shear capacity under plate fracture failure
calibrated with a large number of parameter analyses. A mode
b
simplified model of shear behavior is proposed. Nv, min : the final shear capacity of the high-strength
(3) According to finite element analysis, it can be seen friction bolt connection under different failure
that the shear behavior of high-strength bolts connection modes
presents the isotropic hardening characteristics under Pt: pre-tension of the bolt
cyclic loading. Therefore, hysteretic model and hysteretic Ki: the initial friction stiffness
criterion are obtained. It provides a great tool for the Ke: the unloading stiffness
seismic performance of structure with high-strength bolts A: bp×tp the cross-sectional area for the core plate
connection. L: |lp−lc| the intersection length of the core plate
(4) The model is simple and accurate, which is and cover plate
important for engineering applications. The simplified λ: the Influence coefficient
model provides a basis for modeling high-strength bolts
connection using simple spring element in whole structure
References
analysis.
ABAQUS (2005). ABAQUS User’s Manual, Version 6.5.
Acknowledgments Hibbitt, Karlsson and Sorenson, Inc., USA.
Azuma, K., Chida, T., Tarui T., Matsuishi, N., and Okada, T.
The authors would like to thank the National Natural (2009). “Development of super high-strength bolts with
Science Foundation of China for financially supporting tensile strengths of 1600 to 2000 N/mm2.” International
this research work (Grant No. 90815004). Journal of Steel Structures, 9(4), pp. 291-299.
Chen, Y. Y., Shen, Z. Y., Han, L., Wang, S. N., Liu, C. X.,
Notation Zhang, S., and Huang, Y. Q. (2004). “Measurement of
The following symbols are used in this paper: slipping-resistant coefficients of two coating surfaces in
E; Young’s modulus high strength bolts connections.” Building Structure,
fy: yield stress of steel 34(5), pp. 3-6 (in Chinese).
b Chung, K. F. and Ip, K. H. (2000). “Finite element modeling
fy : yield strength of the bolt
of bolted connections between cold formed steel strips
εy: yield strain
and hot rolled steel plates under static shear loading.”
εy2: strain at the end of the yield plateau Engineering Structures, 22(10), pp. 1271-1284.
εu: ultimate strain Chung, K. F. and Ip, K. H. (2001). “Finite element
fu: ultimate stress investigation on the structural behaviour of cold formed
D(d): the diameter of the bolt steel bolted connections.” Engineering Structures, 23(9),
bp: the width of the core plate pp. 1115-1125.
tp: the thickness of the core plate GB50017-2003 (2003). Code for design of steel structures.
lp: the length of the core plate China Architecture & Building Press, Beijing, China (in
bc: the width of the cover plate Chinese).
fc: the thickness of the cover plate GB50221-95 (1995). Code for inspection and evaluation of
lc: the length of the cover plate structural steel engineering. Architecture & Building
e1, e2: bolt spacing Press, Beijing, China (in Chinese).
la, ba: the distance from the bolt center to the edge of Ju, S. H., Fan, C. Y., and Wu, G. H. (2004). “Three-
dimensional finite elements of steel bolted connections.”
the plates
Engineering Structures, 26(3), pp. 403-413.
µ: friction coefficient
JGJ82-91 (1992). Code for design, construction and
P: reaction force of the loading point acceptance of high strength bolt in steel construction.
δ: displacement of the loading point Architecture Industry Press, Beijing: China (in Chinese)
nf: the number of surfaces transmitting friction Lee, S. H., Kim, J. H., and Choi, S. M. (2009). “Structural
b
Nm : friction force behavior of tension joint with high-strength bolted split-
∑t : the smaller thickness of the pressure plates in tee.” International Journal of Steel Structures, 9(2), pp.
the same force direction (compare tf and 2tc) 93-105.
b
fcu : plates confined strength Li, Q. C., Gu, Q., Su, M. Z., and Chen, A. G. (2003).
An: the minimum of the net section “Experiment of high-strength bolted connection behavier.”
Analysis on Shear Behavior of High-Strength Bolts Connection 213
Journal of Xian University of Science and Technology, clearance.” Composite Structures, 71(2), pp. 159-175.
23(3), pp. 322-324 (in Chinese). Nah, H. S., Lee, H. J., Kim, K. S., Kim, J. H., and Kim, W.
Liu, G., Li, Q. C., and Hu, A. (2009). “Test and modeling of B. (2009). “Method for estimating the clamping force of
the behavior of high-strength bolted connection with sand high strength bolts subjected to temperature variation.”
blasted faying surface.” Journal of Suzhou University of International Journal of Steel Structures, 9(2), pp. 123-
Science and Technology, 22(3), pp. 38-41 (in Chinese). 130.
McCarthy, M. A., McCarthy, C. T., Lawlor, V. P., and Song, M. Z., Xu, J. H., Lu, H. L., and Wang, Y. (2009).
Stanley, W. F. (2005). “Three-dimensional finite element “Experimental study on anti-sliding coefficient of friction
analysis of single-bolt, single-lap composite bolted joints: type high strength bolt connectors.” Industrial
Part I - model development and validation.” Composite Construction, 39(12), pp. 102-104 (in Chinese).
Structures, 71(2), pp. 140-158. Yu, W. K., Chung, K. F., and Wong, M. F. (2005). “Analysis
McCarthy, C. T. and McCarthy, M. A. (2005). “Three- of bolted moment connections in cold-formed steel beam-
dimensional finite element analysis of single-bolt, single- column sub-frames.” Journal of Constructional Steel
lap composite bolted joints: Part II - effects of bolt-hole Research, 61(9), pp. 1332-1352.