ENGR 211 Bridge Design Project
 Preliminary Design of Single-Span
Truss Bridge for Truck Loading
 Select Optimum Material and Cross-Section
 Satisfy Allowable Tensile Stress and
Buckling Criteria
 Satisfy Minimum Cost Criteria
 Utilize the West Point Bridge Designer
Program
Typical Single-Span Truss Bridge
“Pratt Through Truss”
h
4 m typ.
6 bays, or 24 m long
General Scope of Assignment
 The 24 m single-span truss bridge must support the load of
a moving truck with a weight of 40, 000 lb.
 To simplify the design, we restrict the design so that the
lower span has 7 equally spaced joints. These joints cannot
be moved or eliminated. See restrictions on other joints as
presented later.
 Your job is to complete the remainder of the truss structure,
and design the most economical bridge that satisfies
essential design criteria by making the following design
choices:
General Scope of Assignment
 Choose the location of the other joints and place
members connecting these joints.
 Choose the "best" combination of
 materials (A36 carbon steel or A572 high strength
steel),
 cross-section geometry (solid rectangle or tube), and
 the cross-section size (varies, mm).
 Optimize your design for minimum bridge material
cost (see program for cost algorithm).
General Scope of Assignment
 Design constraints include:
 Tension in members cannot exceed a tensile strength
that would cause failure by material yielding, and
 Compressive force in members cannot exceed a
compressive strength that would cause failure by
member buckling.
AASHTO H20-44 Cargo Truck
The AASHTO H20-44 cargo truck has two axles spaced 14
feet (approximately 4.3 meters) apart. The front axle load is
8,000 pounds (approximately 3,600 kg) and the rear axle load
is 32,000 pounds (approximately 14,500 kg). When designing
a bridge for an AASHTO H20-44 loading, the designer must
ensure that all members in the structure can carry the forces
generated by this loading, no matter where the hypothetical
H20-44 truck is positioned on the bridge. The design program
does this for you by spreading the weight over two (or more)
adjacent nodes. The design program does multiple analyses to
simulate the truck moving across the bridge.
The Design Process
 Once you select the joints and members connecting the
joints, the design program will make an initial selection
for the material (carbon steel), cross-section type (solid
rectangle) and cross-section size (120x120 mm).
 The program than performs a systematic truss analysis to
determine the internal force in each truss member
(tension or compression).
The Design Process
 Failure Analysis
 If the member is in tension, the program checks to see if
the member stress (force/cross-sectional area) exceeds the
tensile strength (allowable stress) for the material that has
been selected for that member (failure due to the material
"yielding" or becoming inelastic).
 If the member is in compression, the program checks to
see if the compressive force exceeds the compressive
strength of the member (failure due to physical buckling).
After the program completes the analysis, you may check
you design in three windows at the bottom of the screen.
The Design Process
 Checking Your Analysis:
 The program provides several output “windows”
 Load Test Results (click on right i at the bottom)
 Cost Summary
 Member List
 Examples of these are shown below:
Load Test Results
Member List
Cost Summary
Cost Algorithm
Note that different materials and cross-sections have
different costs per kg of member. Each connection
(joint) has a cost. An overall product cost is added.
The Re-Design Process
If the member fails by yielding, it has failed the
following test P   y A where P is the tensile force in
the member,  is an empirical constant,  y is the yield
stress for the material and A is the cross-sectional area
of the member. Therefore, to reduce the possibility of
failure by material yielding, you may make one or all of
the following changes to your design:
• Choose a material with a higher yield stress  y , or
• Choose a cross-sectional area, A, for the member
that is larger.
The Re-Design Process
If the member fails by buckling, it has failed the following
test: P   2 EI / L2 where P is the compressive force in the
member,  is an empirical constant depending on end
conditions, E is Young's modulus of elasticity for the material,
I is the moment of inertia of the cross-section, and L is the
length of the member. For a rectangular cross-section of
dimension bxh, I  bh3 /12
; and for a tube with outer
diameter Do and inner diameter Di, I   ( Do4  Di4 ) .
Therefore, to reduce the possibility of failure by member
buckling, you may make one or all of the following changes
to your design:
 Choose a material with a larger Young's modulus (E),
 Choose a cross-section with a larger moment of inertia
(I) which means increasing the cross-sectional area, or
 Make the member shorter (L).
The Re-Design Process
If the member is over-designed, e.g., the tensile
force is much less then the allowed tensile strength,
then we may re-design the member using ideas
opposite to that in the above paragraphs. For
example, if the tensile force is much less then the
allowed tensile strength, choose a cross-sectional
area that is smaller, OR a material with a lower yield
stress if cheaper.
There will typically be several options in which to
re-design, so the design process is iterative, or is a
trade-off study between the various options.
Tensile Yielding
of an Elastic Material
elastic bar in tension
A

L
P
L +d
P
 º
A
d
e º
L
axial stress
axial strain
P
y
 y º yield stress
E  Young ' s mouduls
e
Elastic Buckling of a Rod
d
P
P
P  Pcritical
Pcritical 
L
 2 EI
2
L
d
E  Young ' s modulus
P
I moment of inertia
2
r
ò dA
Teams Have Different Problems
 Each team is to work a different problem according to
the following schedule:
• Teams 1-5: All member joints you add must be
greater than 4.5 meters and less than 6.5 m in height.
NO restriction on horizontal location (except those at
0 meters, which are fixed). NO restriction on the
number of joints or members you use.
• Teams 6-10: As above, but 5.0 to 7.0 meters.
• Teams 11-15: As above, but 5.5 to 7.5 meters.
• Teams 16-21: As above, but 6.0 to 8.0 meters.
2-Member Teams
 You are to work in teams of two. Therefore,
from your current team of four, the following
two sub-teams are defined: Arrange your
team alphabetically; then Team A is the first
two in the alphabetical list; Team B is the
other two team members.
 Thus, if you are on team 7, we now have two
2-person teams for the design project: 7A and
7B.
Report Requirements
 Formal written report (word processed document) consisting of
 Summary (short) of the design problem and your design results and
recommendations, and cost [this is what your boss would read to
determine if the rest of the report is worth reading],
 Description of the design problem, requirements, truss loading, etc.,
 General description of how a truss analysis is conducted,
 Description of procedure that your individual team took to reach your
final design, trade-off studies you did, etc.,
 Summary and discussion of the final design details and the cost (the
program will print these for you), with references to design program
results contained in the appendix, and an
 Appendix containing a printed copy of the truss drawing, member list
window, the cost summary window, and the load test results window.
Project Grading
• Maximum score - 100 points
• Satisfactory design - 25%
• Design report - 35%
• Lowest Cost post design - 40%.
– Two teams with the lowest cost designs will receive full credit
(40%),
– next three lowest cost designs will receive 80% of maximum
available design score (80% of 40%),
– remaining teams with the highest cost designs will receive 60% of
the maximum available design score, and
– Failure to meet the assigned design scope or assigned team problem
will automatically place your team in the lowest category (even if
you have the best design!).
Due Date
Thursday, November 30, 10 AM
(no exceptions!)