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Shear Stiffness and Maximum Shear Stress of Tubular Members
P.C.J. Hoogenboom and R. SpaanDepartment of Civil Engineering
and Geosciences, Delft University of Technology
Delft, The Netherlands
ABSTRACT Table 1. Traditional shear formulae for several
cross-sections
Cross-Section Shear Stiffness
sGA
Maximum Shear Stress
max
56
GA 32
V
A
3237
GA 43
V
A
12
GA
A
V2
webGA 15
14 web
V
A
b
h
b
h
2
2 2
10
12
hGA
h b+
2
34 2
4b V
Ah
+
The shear stiffness and the maximum shear stress predicted
bycommonly used formulae are accurate for thin-wall tubes but too
smallfor thick-wall tubes. New formulae for the shear stiffness and
themaximum shear stress are proposed.
KEYWORDS: Shear Stiffness; Shear Stress; Tubes; Pipes;
CircularCross-Section; Frame Analysis
INTRODUCION
Tubular members are frequently used in offshore structures. In
the
analysis of these structures often axial forces in the members
aredominant but also moments and shear forces can be important.
Obviously, the values of the member stiffnesses are needed to
performthe structural analysis and compute the force flow. The
values of the
member section moduli are needed to check the member
maximumstresses. Formulae for shear stiffnesses and maximum shear
stresses are
provided in text books and reference books for various
cross-sections(Table 1) (Timoshenko 1970), (Hartsuiker 2000),
(Blaauwendraad
2002). They have been derived analytically in various ways
includingthe principle of minimum complementary energy. Recently,
the authorsstudied tubular members using finite element analysis
and found thatthe real values can be substantially larger than
predicted by the formula
(Spaan 2003). The formulae for thin-walled tubes were found to
beaccurate. However, the shear stiffness and maximum stress
increasesubstantially with the wall thickness.
TRADITIONAL DERIVATION OF SHEAR FORMULAE
Traditionally, the shear stiffness of a cross-section of a
prismatic beam
is derived by setting equal the complementary energy of a slice
of thbeam to the complementary energy of a slice of the wire model
of thbeam. This method can be used for any cross-section shape. The
firsstep in the derivation is assuming a statically allowable
stres
distribution. A reasonable assumption for a thin wall tube
is
In the next section of this paper the traditional formula for
the shear
stiffness and maximum shear stress in round tubular members
arederived. Subsequently finite element models are used to check
these
formulae. The finite element results on the maximum shear stress
andthe shear stiffness are presented. In the conclusions new
formulae are
max cosx = , (1
proposed for the shear stiffness and maximum shear stress in
roundtubular members.
where x is the shear stress in the circumferential direction of
th
cross-section and max is the largest shear stress (Fig. 1). In
fact it ca
be shown that this is the exact distribution of the shear stress
usincylindrical shell theory (Timoshenko 1959)(Hoefakker 2003).
Th
316
Proceedings of The Fifteenth (2005) International Offshore and
Polar Engineering Conference
Seoul, Korea, June 1924, 2005Copyright 2005 by The International
Society of Offshore and Polar Engineers
ISBN 1-880653-64-8 (Set); ISSN 1098-6189 (Set)
