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Assignment 1:
Pressure loaded deck of a box girder
1 Introduction
Cities of Vancouver and North Vancouver came to agreement to replace the aging Lions gate bridge! You are
working in an engineering company that is bidding for the design contract. Your team needs to propose initial
structural design. Although a few options are proposed, you are in charge of a concept that features three decks:
one for pedestrians/cyclists, one for cars (6 lanes) and one for busses and trains.
At the same time, east of the bridge is Seaspan Vancouver Shipyards, which is designing a new ferry for Seaspan
Ferries! Midship section will be also be a three-level box girder. You realize that similar design principles apply
here as well! Both structures will be made of stiffened panels (plate with reinforcing girders, see Figure 2)
Image credit: https://vancouver.citynews.ca/2019/07/30, https://maritimeoptima.com/public/vessels
Figure 1. Bridge and ferry made of stiffened decks.
2 Technical part
This assignment, as all the other assignments in the course is carried out in teams of two students. Prepare one
report. Both names appear on the report. One of you will upload the report to Canvas – both will get the same
grade.
The deck of the bridge/ferry is 18 m wide and loaded with lateral pressure of 20 kPa. The deck will be designed
as stiffened panel shown in Figure 2. The figure shows a repeating unit of the structure. You need to design
thickness of all structural members, and the distance between girders (a and b), in order for weight of the deck
to be minimal. You can assume that edges are clamped.
Longitudinal stiffener can be a flat bar, L- or T-shaped. Transverse girder has a T shape. Yield stress is 235 MPa;
allowable stress is 175 MPa, Poisson ratio 0.3. Neglect corrosion addition.
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Figure 2. Cut-out from a deck showing the stiffened panel.
Minimum thickness of all plates is 4.0 mm, which corresponds to a stiffener height of about 200 mm. If the
height increases, thickness should too (in approx. equal proportion), however, round all thicknesses to 0.5 mm
and height to 20 mm. Furthermore, Euler-Bernoulli beam theory assumes that length-to-height ratio of a beam
is more than 5.
Tip: When the problem seems complicated, start simple! If you are calculating second moment of area, validate
your model with existing data, or consider a simple structure where you know the answer. E.g. when calculating
second moment of area and neutral axis, start with plate and stiffener that have the same width and height,
then you know that the neutral axis is at their intersection.
2.1 Area weight
Calculate the area weight (kg/m2
) of your panel (top view of the deck). Given the area (axb), calculate total
weight of the plate, longitudinal stiffener and transverse frame; then divide by axb.
Density of steel is 7850 kg/m3
3 Reporting
Follow the IMRAD reporting style: Short introduction, explain methods and how where they used, results
obtained and discussion about the meaning of the results. When few methods are compared, discuss on the
accuracy of each approach, potential reasons for inaccuracy and the reasons for differences, how would the
results be further validated, what would you recommend as following steps in analysis.
Reports should be short; e.g. less than 10 pages in length.
b
a
Area of interest (top view, axb)
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Analysis tips:
1. Develop a spreadsheet that calculates:
a. Sig x, considering stiffener dimensions (L=a, h, …) and plate dimensions (a, b, t)
b. Sig y, considering girder dimensions and plate dimensions
c. Von Mises stress from sig x and sig y, at critical points, to be lower that defined allowable stress
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Point σx σy
Beam theory Plate th. Beam th. Plate th.
1 I consists of stiffener and
plate, Mx at 50% of ‘a’ – – –
2 – – I consists of girder and plate,
My at 100% of 18 m –
3 I consists of stiffener and
plate, Mx at 100% of ‘a’ –
I consists of girder and plate,
but at different z, My almost
at max (‘b’ meters away from
end)
–
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I consists of stiffener and
plate, Mx at 50% of ‘a’,
different z than point 1
–
I consists of girder and plate,
but at different z, My almost
at max (‘b’ meters away from
end), different z than point 2
Yes
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I consists of stiffener and
plate, Mx at 100% of ‘a’,
z from NA to top
Yes
I consists of stiffener and
plate, My almost at max (‘b’
meters away from end), z
from NA to top
–
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I consists of stiffener and
plate, Mx at 100% of ‘a’,
z from NA to top –
I consists of stiffener and
plate, My almost at max (‘b’
meters away from end), z
from NA to top
–