PROBLEMS OF THE ACTION OF CONNECTIONS MADE WITH PINS
Milan Šmak1, Josef Puchner2
Brno University of Technology, Faculty of Civil Engineering,
Veveří 331/95, 602 00 Brno, Czech Republic.
E-mail: 1smak.m@fce.vutbr.cz; 2 puchner.j@fce.vutbr.cz
Abstract. Joints with pin connections are implemented either as the component of the pivot machine components, or,
they are used as connections in the section of steel and timber structures. Connections made with steel pins can have
various geometric configurations; they can be exposed to the static or dynamic actions. Design rules prescribed in the
standard document for design of steel structures EN 1993 may be used in the process of design (or check calculation)
of pin connections. This report summarises the pieces of knowledge and comparisons of the pin connection´s actions
based on the exact theoretical solution of the curving member. Applied design rules are according to EN 1993 and the
experimental tests.
Keywords: pinned connections, pin, connection plate, design, theoretical solution, experimental tests, failure.
1. Introduction
Connections with pins are used not only as parts of
pivot machine components, but they are also designed as
connections of structural elements in steel and timber
structural systems. This category of connections is often
used as connections with mutual free slewing of connected elements.
Connections made with pins can have various geometrical configurations. They can be applied to connections of structural elements stressed by static, dynamic or
fatigue loads.
The simple application rules are declared in the
standard document for design of steel structures EN 1993.
These directives can be used for safe and economical
design of the pin connection. Check on the pin element
and check on the connection plates are two basic parts
when preparing the static design of these connections.
In common case, design of pin connections can be
realized according to standard design rules: the pin and
the plate thickness are designed according to their geometrical dimensions, geometry (dimensions) of the plate
is designed on the basis of its thickness.
Some difficulties may occur in case of minimization
of dimensions of connection plates or in the case of loadcarrying capacity determination of an existing pin connection, i.e. in a situation of non-observance of specified
geometrical conditions.
An example of the pin connection is outlined in the
Fig 1.
Fig 1. The illustrative example of the pin connection
the pin: d = 30mm, material steel S355 , the connection plates: t = t1 = 8mm; a = 15mm; c = 15mm; hole
diameter d0 = 30mm
The load-carrying capacity of the connection made
as a pin connection (in accord with design rules EN
1993):
•
for thickness t = 8mm: FEd ≤ 21.17kN
•
for c = 15mm: FEd ≤ 12.97kN
•
for a = 15mm: FEd cannot be determined because a < 20mm
The load-carrying capacity of the connection made
as a bolted connection with one element (in accord with
design rules EN 1993):
799
•
for e1 = e2 = 30mm: FEd cannot be determined
because e1 = e2 < 1.2 · 30 = 36mm
⎛
σ max = ⎜
⎜
⎝
It stands to reason, that the load-carrying capacity of
this connection is not zero, at least in case of the static
stressed connection without dynamic and fatigue influences. It is possible to conclude, that design rules for
connections with pins, specified in EN 1993, are very
conservative.
FEd
2
M⎞ 1
⎟⋅
−
rs ⎟⎠ A
+
c
M ⋅ rs
2
⋅
c
I
rs −
2
(1)
where rs is the average radius
c is the length of the lateral part of the plate (Fig 2)
A is the cross-section area
I is the second moment of inertia
The plate of a pin connection is deformed by the effect of load; the deformation in the transverse direction
(beside elongation) induces reducing of the clearance
between the pin surface and the edge of the plate of the
connection. As long as this clearance exists, the bending
moment in the main section of the plate (Fig 2) is determined by:
2. Theoretical solution
The theoretical solution of this problem results from
the classic theory of curved bars [1]. The plate of a connection with a pin can be regarded as a curved bar – this
results in outside – inside radius ratio R/r0 = 5/1 (Fig 2).
It means, that the effect of the tensile force FEd is added to
the effect of the bending moment. The stress behaviour in
the main section of the connection plate (i.e. in the cut
across the centre of gap in perpendicular direction to the
acting force – Fig 2) is not constant, but there is the stress
maximum σmax in the inner side of the cross-section –
Fig 2.
The stress value σmax is given by:
M=
1
⎛ π
−
⎜
π⎝
2
⎞
(2)
1⎟ ⋅ FEd ⋅ rs
⎠
If the plate deformation in main section of the plate
reaches the clearance level, the bending moment (2) is
reduced to the value:
M=
1
⎛ π
⋅⎜
−
⎝ 2
π
⎞
1
⎠
π
1⎟ ⋅ FEd ⋅ rs −
⋅
Q ⋅ rs
(3)
where Q is the radial force acting from the pin to the plate
in the main section of the plate.
As a consequence of this reduction the modification
of the top of stress in view of the uniform stress is:
σn =
FEd
2 ⋅ (R − ro ) ⋅ t
=
FEd
2⋅c⋅ t
(4)
To simplify the calculation of maximal stress σmax,
the coefficient of stress concentration α is defined:
α=
σ max
σn
(5)
The coefficient α is a function of the outside radius
R and inside radius r0 of the connection plate:
λ=
R
ro
(6)
The following expressions formulate coefficients α –
λ relation.
According to [2]:
2
3
1
6
α≈ + ⋅
λ −1
λ +1
⋅ ln λ − 1
2 ⋅ (λ − 1)
(7)
This formula gives lower values of stress than the
modified formula by authors:
2
3
Fig 2. Stress behaviour in the plate of a connection
with a pin, description of geometrical parameters, flow
of forces behaviour
α= +
800
1
⋅
5.5
λ −1
λ +1
⋅ ln λ − 1
2 ⋅ (λ − 1)
(8)
Fig 3. Effects of α-factor on the ratio of outside radius R and
inside radius r0 (r0 is constant, R is variable)
The calculated relationship curves for connections
with clearance and without clearance round a pin are in
agreement with the value λ ≈ 3 (Fig 3).
The expression for the moment M, which acts in the
vertical section of the plate across the point of load:
M=
1
π
⋅
FEd ⋅ rs
Fig 4. Geometrical and material configurations of
specimens
Configuration of specimens and load tests:
•
The pin:
•
material steel S355 (11 523)
•
diameter d = 29.8mm
•
The plates:
•
material steel S235 (11 373)
•
thickness t = 7.85mm
•
pl;ate width b = 90mm, 76mm, 60mm
•
fy = 280MPa, fu = 380MPa
•
material steel S355 (11 523)
•
thickness t = 7.90mm
•
plate width b = 90mm, 76mm, 60mm
•
fy = 348MPa, fu = 532MPa
•
material steel S690 (Weldox 700)
•
thickness t = 7.75mm
•
plate width b = 76mm, 60mm
•
fy = 771MPa, fu = 834MPa
•
drilling diameter d0 = 30mm, 31mm,
32mm, 33mm
(9)
This moment is about 1.75times greater than the
moment in the main section of the connection plate, nevertheless the normal force does not act. There exists a
compression stress in the contact spot between the pin
and the connection plate, the magnitude of this stress
depends on the pin clearance in the gap.
Although compression stresses in the vertical section
are greater than tensile stresses in the main section, their
effect is less dangerous than tensile stresses. Therefore
the failure of the plate occurs in the main section.
3. Experimental solution
The set of experimental load tests of pin connections
was realised on the basis of numerical solution of the
given problem. The main aim of these tests was to verify
the acquired knowledge of behaviour of pin connections.
More than 100 experimental specimens in various
geometrical and material configurations were tested. Geometry and dimensions of specimens are described in the
Fig 4.
Pin connections were tested under static load with a
continuous tensile force increase. Free mutual slewing of
connected elements was respected. The influence of various geometrical parameters a and c and various drilling
for the pin (i.e. clearance between the pin surface and the
edge of the plate) on the load carrying capacity was researched.
Real geometrical parameters of specimens were
measured. Real material characteristics were determined
by material tests of standard specimens.
Fig 5. The test set – the pin and the plate before loading test
801
Fig 9. The failure connection plates of 90 mm width
after loading test. There are plates from steel S235,
S355 and S690 with drilling of 33mm on the left side.
Conclusions
The aim of this paper was to acquire a more detailed
concept of behaviour of connections with pins under
static load.
It is possible to conclude, on the basis of results of
this study, that design rules EC 1993 for design/check
calculation of a pin connection under the influence of
static loading do not give sufficiently accurate results of
static analysis.
The load-carrying capacities of the connections are
obviously lower in comparison with loading tests results.
Design rules EN 1993 cannot be used for small dimensions of plates (dimensions a, c). The using of theoretical
or experimental solution is possible in this case.
Fig 6. The test set – the pin and the plate in the testing
machine before loading test
Tab. 1. Summary of selected results
specimen
drilling
FRd,pin
FRd,bolt
width
material
[mm]
[kN]
[kN]
60mm
S235
30
0
0
17,2
96,5
31
0
0
16,2
93,6
32
0
0
15,2
90,9
33
0
0
14,2
87,3
30
0
0
24,2
125,4
31
0
0
22,8
123,7
32
0
0
21,4
120,5
33
0
0
20,0
120,4
30
0
0
37,2
170,7
31
0
0
35,0
165,4
32
0
0
32,9
162,7
33
0
0
30,9
156,2
30
13,2
55,4
29,3
128,4
31
8,1
50,3
28,2
128,0
32
2,9
45,7
27,2
127,4
33
0
0
26,1
124,6
Fig 7. The failure connection plates after loading test.
The tensile failure occured in the side section of the
plate. There are plates from steel S235 with drilling of
33mm on the figure.
S355
S690
76mm
S235
S355
S690
Fig 8. The failure connection plates of 60mm width
after loading test. There are plates from steel S235,
S355 and S690 with drilling of 33mm on the left side,
and 30mm (in the same order) on the right side of the
figure.
90mm
S235
S355
802
FRd,theoret Fpl,Rd,test Fel,Rd,test
[kN]
[kN]
30
16,5
78,1
41,2
165,4
31
10,1
70,9
39,7
163,3
32
3,7
64,4
38,3
160,8
33
0
0
36,8
159,5
30
35,9
120,1
63,4
227,8
31
21,9
109,1
61,1
223,5
32
8,0
99,1
58,8
218,0
33
0
0
56,6
214,2
30
44,0
88,9
41,4
158,0
31
38,8
81,4
40,4
155,7
32
33,7
74,6
39,4
155,2
33
28,6
68,5
38,3
149,6
30
55,0
125,2
58,4
198,1
31
48,6
114,6
56,9
195,1
32
42,2
105,1
55,4
190,9
33
35,7
96,5
53,9
187,9
[kN]
71,1
69,0
67,0
64,3
82,0
80,9
78,8
78,8
152,5
147,7
145,3
139,5
94,6
94,3
93,9
91,8
108,2
106,8
105,2
104,3
203,5
199,6
194,7
191,3
116,4
114,7
114,4
110,2
129,6
127,6
124,9
122,9
•
The real geometrical parameters of the plate and the
real material characteristics were determined.
When FRd = 0, the minimal dimensions were not respected:
e1 = e2 ≥ 1,2 · d0
a ≥ 2/3 · d0
c ≥ 1/3 · d0
Fel,Rd, test is the elastic load-carrying capacity of
the pin connection from the static loading tests.
Fel,Rd, test is the extreme tensile force in the elastic zone of the material.
FRd [kN]
140,00
120,00
The results of theoretical solution, experimental
loading tests and static analysis according to design rules
of EN 1993 are presented in the Table 1.
100,00
80,00
60,00
FRd [kN]
120,00
40,00
100,00
20,00
30
80,00
S355,pin
31
S355,bolt
32
S355,teor
S355,test
33
drilling[mm]
Fig 11. Steel S355 – comparison of FRd (connection
plates of 90 mm width)
60,00
40,00
Acknowledgments
20,00
30
S235,pin
31
S235,bolt
32
S235,teor
S235,test
33
This research has been supported by projects of
GACR No. 103/09/1258 and by Research Plan MSMT
reg. No. MSM 0021630519.
drilling [mm]
Fig 10. Steel S235 – comparison of FRd (connection
plates of 90 mm width)
References
where:
•
FRd, pin is the load-carrying capacity of the pin
connection – [4], part 3.13.
•
FRd, bolt is the load-carrying capacity of the connection, the pin connection is analysed as the
bolted connection with one element – [4], part
3.6.1.
•
FRd, theoret. is the ultimate tensile force in the
plate according to theoretical solution (σn =
σmax) – part 2.
•
Fpl,Rd, test is the total load-carrying capacity of
the pin connection. Fpl,Rd, test is the extreme
value of the attained tensile force in the connection, obtained from the experimental test.
Timošenko, S.P. 1951. Pružnost a pevnost. Praha: Technickovědecké vydavatelství.
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Part 1-1: General rules and rules for building, Praha:
ČNI, 2006 .
ČSN EN 1993-1-8: Eurocode 3: Design of steel structures –
Part 1-8: Design of joints, Praha: ČNI, 2006.
ČSN EN 1993-1-12: Eurocode 3: Design of steel structures –
Part 1-12: Additional rules for the extension of EN 1993
up to steel grades S700, Praha: ČNI, 2008.
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