Exercise 5

NTNUNorwegian University of Science and Technology.

Faculty of Marine Technology

Department of Marine Structures. TMR4205 Buckling and Collapse of StructuresRestrained - and flexural torsional buckling________________________________________________________________________________________________Date: February 2011 Signature: EKim Distributed Date: 26.02.11 Due Date 07.03.11Problem OneFor the L-profile shown in Figure 1a, derive the critical load expression for restrained torsional buckling as given by Equation (2.159) in the compendium. Use the expression for pure torsional buckling (Equation (2.140)). For this purpose use the virtual extension of the profile as shown in Figure 1b.

Figure 1. An L-profile of a Ship Stiffener.

Problem twoIPE270 was found to satisfy the design criteria against flexural buckling ((Y = 240MPa) for a 9m column at 390KN compressive load.

Assume, hypothetically, that the flanges of that profile are moved so as to form a channel section (see Figure 2). Check whether the profile now is strong enough with respect to flexural-torsional buckling.

Figure 2.Given:Shear center with respect to web (not center of gravity), yo, and the polar moment of inertia, Ip.

Table 1.CONTINENTAL IPE SECTION *see key below

sizeDIMENSIONSWT per metre M KgSection A cm sqr.

hmm bmm amm emm rmm hmm

8080463.85.25606.07.64

100100554.15.77758.110.3

120120644.46.379310.413.2

140140734.76.9711212.916.4

160160825.07.4912715.820.1

180180915.38.0914618.823.9

2002001005.68.51215922.428.5

2202201105.99.21217826.233.4

2402401206.29.81519030.739.1

2702701356.610.21522036.145.9

3003001507.110.71524942.253.8

3303301607.511.51827149.162.6

3603601708.012.71829957.172.7

4004001808.613.52133166.384.5

4504501909.414.62137977.698.8

50050020010.216.02142690.7116.0

55055021011.117.224468106.0134.0

60060022012.019.024514122.0156.0

CONTINENTAL IPE SECTION - KEY

1

_937901439.doc

y

z

h

b

s

t

_937902816.unknown

_937900067.doc

(b)

(a)

2h

h