FEM AND FVM APPLICATIONS CEP # 2

Problem
Design Project Size the members of the bridge shown in the accompanying figure for a case
in which traffic is backed up with a total of four trucks equally spaced on the bridge. A typical
truck has a payload weight of 64,000 lb and a cab weight of 8000 lb. As a starting point, you
may use one cross section for all beam elements. You may also assume one cross section for
all truss members. The roadbed weighs 1500 lb/ft and is supported by I-beams. Use standard
steel I-beam sizes. Design your own truss configuration. In your analysis, you may assume
that the concrete column does not deflect significantly. Write a brief report discussing how
you came up with the final design.

Grading Criteria Attained

 Literature Review
 Understanding Of the Problem
 Market Survey and Cost Analysis
 Fe Tool and Hand Calculation
 Valid Conclusions

Group Members
Faizan Samdani (AU 19005)
Khwaja Muhammad Abdullah (AU 19011)
Mujtaba Sheikh (AU 19013) Submitted to
Sheeraz Shahid (AU 19022) Dr. Faraz Akbar
LITERATURE REVIEW
Trusses:

A truss is a structure that has multiple members connected to each other so that each and
every member combines and forms as a unit structure, it’s application is wide over in the
construction industry and it is used in roof, bridges as it transfers the load over a wide region
in order to attain safety and avoid failure of the materials. Different types of trusses
configuration are mentioned below, the design we are using will have truss design simialr to
pratt and warren.

Beams
Beams and columns are two important types of structural elements that play a key role in
creating a safe load path to transfer the weight and forces on a structure to
the foundations and into the ground. Beams and columns could be built using the same
shapes and materials but each serves a different function and is designed differently.
TRUSS BRIDGE
Truss bridge is a type of bridge whose main element is a truss which is a structure of
connected elements that form triangular units. Truss is used because it is a very rigid structure
and it transfers the load from a single point to a much wider area. Truss bridges appeared
very early in the history of modern bridges and are economic to construct because they use
materials efficiently.
Before Industrial revolution (19th century), almost all bridges in use were made of stone. But
wood and iron can resist tension and compression better and stone and United States had
much wood so they made many wooden bridges in those times and most of them were truss
bridges. Town's lattice truss, a very simple variant of truss, was patented in 1820. First half of
19th century saw very few truss bridges made of iron although the first patent for an iron
truss bride was issued to Squire Whipple in 1841. But metal slowly started to replace wood,
and wrought iron bridges started appearing in the U.S. in the 1870s only to be replaced by
steel in 1880s and 1890s. In time some places (like Pennsylvania) continued building truss
bridges for long spans well into 1930s, while other (like Michigan) started building standard
plan concrete girder and beam bridges.
Material Selection
We have used steel as our material of both trusses and beam. Steel bridges are widely used
around the world in different structural forms with different span length, such as highway
bridges, railway bridges, and footbridges. The main advantages of structural steel over other
construction materials are its strength, ductility, easy fabrication, and rapid construction. It has a
much higher strength in both tension and compression than concrete, and relatively good strength
to cost ratio and stiffness to weight ratio. Steel is a versatile and effective material that provides
efficient and sustainable solutions for bridge construction, particularly for long span bridges or
bridges requiring enhanced seismic performance.

MATERIAL SPECIFICATIONS MATERIAL STRUCTURAL STEEL

YOUNG’S MODULUS 30457925 lb/in2
POISSON’S RATIO 0.3
DENSITY 0.283 lb/inˆ3
COEFFICIENT OF THERMAL EXPANSION 1.17e-005 Kdeg
YIELD STRENGTH 43511.3 lb/in2

Material Cost Calculation

A steel I-beam can be easily found from your local steel supplier. If you need just one length of I-
beam you may be able to have them cut in different lengths from a scrap piece they have left over
from a large shipment. This will cost anywhere from $.90 to $1.25 per pound. That means you
can purchase a roughly 6 feet in length for a cost of $112.50 to $187.50. Taking mean of these 2
values and multiplying it by the value of PKR, we will get PKR for 6 ft. length of I beam:

Calculation for 200 ft. of I beam

We estimate around 1,000,000 PKR to be estimated cost of this bridge project after adding the
variable cost such as transportation, manual labor, contractor etc.
Understanding of the problem
The following task is related to solve two of the main problems, designing memebers of the bridge
and a truss design which helps in reducing the deflection in the road due to load of trucks equally
spaced.
The main results is to show how sizing of the cross section can results in variation in deflection and to
how much the road deflects under loading.
A typical beam trus bridge spans about 39 ft in width. Therefore we assume that our bridge do not
crosses a wifth of 39 ft. while the other dimensions were taken from the question that is length.
It is described that a four equally spaced trucks are on the bridge each having length of 25ft payload
and 10ft cab that is 35 ft. and in total exerting a force of 72000 lb load each.
1 cab and truck = 72000 lb
Roadbed=1500 lb/ft

Usually a roadbed is constructed using 4 I beams, therefore we assume all of the load is distributed
among 4 I beams equally and that we can solve for I beam by dividing the overall load by 4.
Also to simplify our calculation we assume that for a safe bridge design it is important to have a
safety allowance for vehicles that is what if more than 4 trucks are on the bridge or what if they are
unequally spaced, therefore we assumed that all the trucks distribute weight equally on the whole
length of the bridge.

Therefore 1 truck load = 64000 + 8000 = 72000 lb.

4 trucks = 72000*4= 288,000 lb. (on 4 beams)
4 trucks load = 288000/4 = 72000 (on 1 beam)
Converting Trucks load weight into UDL
That is total length of the bridge 200ft

Therefore Truck UDL= = 360 𝑙𝑏/𝑓𝑡

Roadbed load= 1500 lb/ft (on 4 beams)

/
Therefore on 1 beam = = 375 𝑙𝑏/𝑓𝑡

Cumulative load of roadbed and truck on 1 beam therefore equals

= 360+375= 735 lb/ft = 61.25 lb/in

Neglecting the truss for now to know the deflection occur in beam before the truss, it’s FBD can be drawn

L= 200ft

61.25lb/in

Cross Section Of Beam :

A comparative analysis is done by taking different standard of I beam cross section as the objective of
the project requires the sizing the members of the bridge.

Flange, Web Width Depth Area

1.07,0.65 15.8 38.7 58.7 in2
4 20 30 248 in2
7,6 50 80 1024 in2

Material Used
Structural Steel Young Modulus = 200 GPa = 30457925 lb/in2

Calculations Using FEM Software (Ansys APDL)

The following beam is then solved in Ansys APDL and also manually using FEM method described
in the book. Using Following specifications, the results show is the first shown without the truss to
indicate the deflection in beam only and then the deflection on beam after adding the truss
We obtain three results of deflection on 3 cross sections of I beam Sizes
 Areas Deflection in (inches)
58.5 in2 11.9
248 in2 5.3
1024 in2 0.16

That is evident that we’ll opt for the beam that has an area
of 248 in2

Designing the Truss Members

Dimensions
Outer Radius = 5in
Inner Radius = 3in

FE TOOL

FEM ANALYSIS
Following truss configuration is used to solve the problem. It is a good solution as this truss is finely connected
all of its member and hence it will transfer it’s nodal forces very efficiently to each of its members
Applying fixed support on both the sides and on the lower side of truss to imitate the stiffness of
concrete which was very neglible and applying the total load of 61.25 lb/ in.

DEFLECTION RESULTS
We refined our truss design by adding links diagonally to connect the lower points with the upper
points, the difference in both the design are not much changed except the deflection without the
additional linkages was 0.036 inches against the design with linkages that has a deflection of only
0.012 inches

Conclusion
The truss we’ll be selecting is on the left above as there is not a visible difference of deflection of
after and before adding the truss, also it will cost us less than the right as it requires additional 6
linkages and it only increase the cost therefore the best choice is justified, also the stress is equally
distributing among the truss from the beam therefore the beam is safely designed, to simplify our
calculation we distributed the load of 4 trucks equally on the whole beam as it is not necessary that
only four trucks will be at a time on road, so by taking uniformly distributed load we have left
allowances for additional vehicle and the bridge is still showing deflection way under 1 therefore our
bridge design is completely safe to use