Designing paper straw bridge (lightest at ARU - 2.1g). Designing in inventor, Finite Element Modelling and Analysis - ANSYS , Stiffness matrix and constructing a final product.

1. Bridge Assignment
MOD002668
Stress & Dynamics
Submitted By:
Anglia Ruskin Students
1227201
1227204
1231349
1348891

2. Acknowledgment
We would like to acknowledge Dr. Rajshree Mootanah, from Anglia Ruskin University for the efforts & helping to
guide through the project, Dr Mehrdad Asadi for helping the group in understanding and teaching every bits of Ansys
Workbench for finite element modelling, the team which has put a great effort day and night to construct the
lightest bridge for the 2014-2015 bridge project & all the instructors & supervisors who assisted us in understanding
a market based research model.

3. 1
Contents
Introduction ............................................................................................................................................................................... 2
Aim:............................................................................................................................................................................................ 3
Objective: ................................................................................................................................................................................. 3
Purpose & Scope: ...................................................................................................................................................................... 3
Methodology: ............................................................................................................................................................................ 4
Theory: ..................................................................................................................................................................................... 6
Inventor Designs ................................................................................................................................................................ 6
Ansys Workbench Interpretations.......................................................................................................................................... 8
Iteration 1.......................................................................................................................................................................... 8
Stress ................................................................................................................................................................................. 9
Deformation .................................................................................................................................................................... 10
Iteration 2........................................................................................................................................................................ 10
Stress ............................................................................................................................................................................... 10
Deformation .................................................................................................................................................................... 11
Stress Graph for iteration 2.............................................................................................................................................. 12
Physical Model..................................................................................................................................................................... 12
Calculation: .............................................................................................................................................................................. 14
Hand Calculation.............................................................................................................................................................. 16
Step 1: To find the forces ................................................................................................................................................. 16
Step 2: To find the stiffness matrix we need to use the following formula....................................................................... 18
Ansys 2D Calculation Results.................................................................................................................................................... 21
Reactions ......................................................................................................................................................................... 21
Forces per element 2D modelling..................................................................................................................................... 21
All the Forces & Stress in 2D modelling ............................................................................................................................ 22
Test Day Results & Pictures: ..................................................................................................................................................... 23
Conclusion................................................................................................................................................................................ 24
References ............................................................................................................................................................................... 25
Appendix.................................................................................................................................................................................. 26

4. 2
Introduction
The term γέφυρα, which originally means bridge in Greek, was informally more known to be a road over a river. Bridge as the
term gradually changed with time is more commonly now known as a mechanical structure built to overcome physical
hindrances (such as gaps, river, road & even sea).
21st
century has seen some of the extravagant designs in generation to construction of bridges. From Roman arc bridge spanning
over a very small artery of a river (fig 2) to the gigantic suspended bridges like one of Millau Viaduct in the southern France (fig1)
Figure 2 Roman Arc bridge
Figure 1 Millau Viaduct of France

5. 3
The bridges have not only changed the economy of the global world (increasing opportunities) but also explored the heights of
sustaining extreme physical conditions of stress, kinematics & dynamics. An essential factor in constructing a bridge is sound
knowledge of understanding its strength in existing form. Understanding the elastic response under stress. Analytical methods
have proved to be more convenient methods of understanding a bridge. (VDOT, 2014)
Aim:
The bridge project aims to design and construct a paper bridge made of straw/s. The bridge is supposed to sustain a kilogram of
load along with a loading plate for at least a minute without failing.
Objective:
The project shall acknowledge the iterations, designing the 2d/ 3d model on Inventor and analysis the static physical conditions
with its effects determined on computing software Ansys workbench to design the best possible model from materials available.
Purpose & Scope:
The initial purpose of the project is to study, establish and construct a bridge using a convenient, reliable and accurate method
of calculation of the stress distribution, deformation and effect on the application of load. Generate an iteration model and
analyze on finite element analysis software and hand calculation. Secondary objective is confirming the results of the iteration
and finally constructing a modified bridge. (Chen, 1993)

6. 4
Methodology:
The researchers’ brainstormed ideas of creating different designs for the bridge (refer appendix) which includes arc, truss,
cantilever, suspended, tied bridges. However, for the simplicity of the design, it is later decided to build a truss bridge. Following,
the iterations were created which showed the deformations and the maximum equivalent stress on the trusses. The iteration
designs were generated on the inventor.
The obtained results helped in formulating the final bridge with eliminated the drawbacks. Long hand calculation was performed
for individual truss stress and forces for the iteration.
Workbench, ANSYS Version15.0 was selected to run a test model of the iteration. ANSYS CAE helped in better understanding of
the behaviour regime of the soft wood properties. Complete analysis of the model requires a collective description of the
following:
Material: Soft Wood (paper straw solid)
Boundary Conditions: Gap & weight specifications
 Length of the gap to be covered is 300mm
 The width of the gap span should not be exceeded
beyond 150mm
 Weight on the bridge is 1 Kg
 Time 1 minute.
 Weight of the loading plate 0.057 kg
Material properties:
Density – 700 Kg/m3
Young’s modulus – 8000 M Pas(1)
Poisson’s Ratio: 0.3
Yield strength – 5 M Pas
Figure 4 Properties fed in Ansys Engineering data
Figure 3 Bridge Gap Specification

7. 5
The results of the finite element modelling is then compared and scrutinized to achieve the following results:
 Comparing the finite element model with the hand calculations.
 Using the simple rules of the calculation to determine the forces on every trusses.
 Determine the actual region of stress concentration where cracking/ bent occurred.
 Determine the deflection in the bridge.
 Safety factor of the bridge.
Point where Stress & strain are
no more linear. Strain increases
drastically in comparison to
Stress.
Figure 5 Isotropic hardening, showing the yield point where the material breaks off

8. 6
Theory:
The basic concept of the bridge was designed as a 2D design initially. Inventor was used to generate the 2D sketch for the
iteration. Using symmetry the bridge was constructed in 3D model and saved as “.ipt” file.
Inventor Designs
1st
Iteration:
Length of the base: 357 (all dimensions in mm)
height: 92
Projections shown below
Figure 6 Iteration 1 2D projections

9. 7
2nd
Iteration (all dimensions in mm)
Length: 357
Height: 92
Projections shown below
Figure 7 Iteration 2 2D projections

10. 8
Ansys Workbench Interpretations
The file was analysed on the Ansys finite element analysis using workbench. The model (iteration) was meshed up to 2mm mesh
(refer appendix) size to obtain least Skweness and higher element quality (fig 8). The symmetrical ends were fixed while the load
was applied on the top end of the straws. The model has been ignored for any use of the external fluids for the joints
(considering negligible).
Iteration 1
The model 1 consists of the bridge with trusses and a support in the centre sideways.
Mesh
Figure 8 finite meshing of the Iteration 1 as sample, 1227201
Mesh size 1.50 mm
Mesh quality Maximum elements lie between 0.75 to 1
Skweness (refer applendix) illustrates that the mesh has been perfect for the analysis. It is highly recommended to have at least
3 layers of mesh to get more accurate results.
Figure 9 Element quality of the mesh

11. 9
Force applied: 10.33 in the negative Y direction.
Stress
Figure 10 Equivalent stress
Interpretation:
Application of the force on the top of the bridge in the negative Y direction resulted in the stress being distributed. The straw
supporting the both sides of the bridge has the highest value of stress 1.64046 MPa. There are still visible stress varying
between 0.35662 to 0.71318 MPa with in the joints (fig 10)
Figure 11 Stress graph with respect to time

12. 10
Deformation
Figure 12 Deformation due to load
Interpretation:
The force deforms the central joint the most up to 0.037587mm. This indicates that there is higher stiffness and the model
eventually would fail as it would break because of high stress concentrations in the middle straw/s (fig 12)
Iteration 2
Iteration 2 has the middle support side missing.
Forces were applied in the negative Y direction equally distributed on the paper top joints and paper straws. The load was
distributed on the top surface while the base ends (all 4) are termed as fixed support.
Stress
Figure 13 equivalent stress

13. 11
Interpretation:
The uniform load initiated a high (red color) stress region shown in the fig 14. However the bridge has a high stress of 2.03M Pa
at the center when the load was applied. However the region around the base supporting both the sides of the bridge has a
varying stress of 0.45148 to 0.67715 MPa around the areas of the joint/s.
Deformation
Figure 14 Total deformation
Interpretation:
On applying the load, the bridge deforms a maximum of 0.048996 mm shown in the red region at the supporting center of the
load. This clearly indicated that the bridge will collapse from the center pulling the sides inside. There are visible changes in the
side straws which connect the joints (fig 15)
Figure 15 Zoom in view for deformation

14. 12
Stress Graph for iteration 2
Figure 16 Stress graph
Physical Model
Step 1 (Rough Final model): Concentrating on the design and generation of the light weight bridge, the researchers decided to
construct a rough model of the final bridge which was intended to carry at least 1Kg of load without the loading pad (fig 17)
Figure 17 First attempt for final bridge
However a lot of glue was used which resulted in the weight of the bridge 3.6 g

15. 13
Step 2 (Less glue): The focus was on using less glue. Quiet certain that only one straw can be used as the base and less than 2
straws could be used to make the side slings to hold the weight, the designed focused on making it lighter, stronger and robust.
Figure 18 Bridge with less glue and straws
Step 3 (Removing instability): The final concern was the instability since the use of only one straw as a base line. Improving the
ends, making them little wide and flat while using the least possible glue, the changes were introduced. This helped to increase
more stability and the loading plate could easily fit in (fig 18).
Step 4 (Final Design):
The final bridge was at last constructed keeping in considerations with all the results obtained from hand calculations of the
iterations, Ansys finite element analysis and the final rough cut models. The result obtained is shown below.
Figure 19 Final model

16. 14
Calculation:
Ansys 2D calculation
Step 1: Draw the points on the work sheet and join the points.
Figure 20 ANSYS Mechanical ADPL 2D generation
Step 2: After joining add the force & calculate / run the program to determine the deformation.
Figure 21 Appling load

17. 15
Step 3: Obtain the deformation and save the file.
Step 4: Import the calculations on the 2D format page.
Figure 22 Stress on the elements
Interpretation: The figure shows that the maximum deformation occurs in the middle support in the region of red. Whereas the
least occurs in the region of blue.

18. 16
Stress in the elements 2D representation:
Hand Calculation
Step 1: To find the forces

19. 17
𝑃
𝐵
= 𝑡𝑎𝑛45°
𝑃 = 85 × 𝑡𝑎𝑛45°
𝑃 = 85𝑚𝑚
𝑀𝑜𝑚𝑒𝑛𝑡 = 𝐹𝑜𝑟𝑐𝑒 × 1
−𝑅1 × 170 − 𝐹1 × 85 = 0
−170𝑅1 − 85𝐹1 = 0
𝑅1 + 𝑅2 = 10.33
𝑀𝑜𝑚𝑒𝑛𝑡 𝑎𝑡 𝑅2
−𝑅1 × 340 + 10.33 × 170 = 0
−𝑅1 × 340 + 1756.1
𝑹𝟏 = 𝟓. 𝟏𝟔𝟓𝑵 √
−5.165 × 170 = 𝐹1 × 85
𝑭𝟏 = −𝟏𝟎. 𝟑𝟑𝑵
∑ 𝑓ℎ = 𝐹3 + 𝐹2 × 𝑐𝑜𝑠45° = −10.33𝑁
𝐹1 + 𝐹3 + 𝐹2𝑠𝑖𝑛45 = 0
−10.33 + 𝐹3 + 7.3𝑠𝑖𝑛45 = 0
∑ 𝑓𝑣 = 𝑅1 − 10.33 + 𝐹2 × 𝑠𝑖𝑛45° = 0
5.165 − 10.33 + 𝐹2 × 𝑠𝑖𝑛45° = 0
𝐹2 × 𝑠𝑖𝑛45° = 5.165
𝑭𝟐 = 𝟕. 𝟑𝑵
∑ 𝐹𝑦 = 𝐹𝑦 × 𝑠𝑖𝑛45° = 5. 𝑁
𝐹4 = −7.304
∑ 𝐹𝑥 = −𝐹𝑦 × 𝑐𝑜𝑠45° = 𝐹5
𝐹5 = −5.165
−10.33 + 𝐹3 + 7.3 × 𝑐𝑜𝑠45° = 0
𝐹3 = 10.33 − 7.3 × 𝑐𝑜𝑠45°
𝑭𝟑 = 𝟓. 𝟏𝟔𝟖𝑵
Finding Stress in each Element Section
𝜎1 =
𝑓1
𝐶𝑟𝑜𝑠𝑠 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴𝑟𝑒𝑎(𝐴)
=
−10.33
0.0000384
= −269010𝑃𝑎 = −𝟐𝟔𝟗. 𝟎𝟏𝑴𝑷𝒂
𝜎2 =
𝑓2
𝐶𝑟𝑜𝑠𝑠 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴𝑟𝑒𝑎(𝐴)
=
7.3
0.0000384
= 190104𝑃𝑎 = 𝟏𝟗𝟎. 𝟏𝟎𝟒𝑴𝒑𝒂
𝜎3 =
𝑓3
𝐶𝑟𝑜𝑠𝑠 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝐴𝑟𝑒𝑎(𝐴)
=
−5.168
0.0000384
= −134586𝑃𝑎 = 𝟏𝟑𝟒. 𝟓𝟖𝟔𝑴𝑷𝒂

20. 18
Step 2: To find the stiffness matrix we need to use the following formula
--------------------------- (1)
Note: Taking angles as clockwise to be positive for all Θ
Stiffness Matrix for element 3:
E3 = 8,000,000,000 Pas
A3 = 0.00003848 m2
L3 = 0.1202 m
Θ = 315O
l = cos Θ = 0.707
m = sin Θ = -0.707
Using formula give above in (1) ----------- we get
0.499849 -0.499849 -0.499849 0.499849
2561331.11
-0.499849 0.499849 0.499849 -0.499849
-0.499849 0.499849 0.499849 -0.499849
0.499849 -0.499849 -0.499849 0.499849
Further Solving, we get:
E= 8000000000 Pas
Area= 3.85E-05 m2
Length= 0.1202 m
Stiffness K = ( EA/L) 2561331.11
1280278.80 -1280278.80 -1280278.80 1280278.80
-1280278.80 1280278.80 1280278.80 -1280278.80
-1280278.80 1280278.80 1280278.80 -1280278.80
1280278.80 -1280278.80 -1280278.80 1280278.80
3

21. 19
Stiffness matrix for Element 1
E1 = 8,000,000,000 Pas
A1 = 0.00003848 m2
L1 = 0.1202 m
Θ = 45O
l = cos Θ = 0.707
m = sin Θ= 0.707
0.499849 0.499849 -0.499849 -0.499849
2561331.11
0.499849 0.499849 -0.499849 -0.499849
-0.499849 -0.499849 0.499849 0.499849
-0.499849 -0.499849 0.499849 0.499849
1280278.80 1280278.80 -1280278.80 -1280278.80
1280278.80 1280278.80 -1280278.80 -1280278.80
-1280278.80 -1280278.80 1280278.80 1280278.80
-1280278.80 -1280278.80 1280278.80 1280278.80
Stiffness matrix for Element 2
E= 8000000000 Pas
Area= 3.85E-05 m2
Length= 0.1202 m
Stiffness K = ( EA/L) 2561331.11
1
2

22. 20
E2= 8,000,000,000 Pas
A2 = 0.00003848 m2
L2 = 0.1202 m
Θ = 225O
l = cos Θ = -0.707
m = sin Θ = -0.707
0.499849 0.499849 -0.499849 -0.499849
2561331.11
0.499849 0.499849 -0.499849 -0.499849
-0.499849 -0.499849 0.499849 0.499849
-0.499849 -0.499849 0.499849 0.499849
1280278.80 1280278.80 -1280278.80 -1280278.80
1280278.80 1280278.80 -1280278.80 -1280278.80
-1280278.80 -1280278.80 1280278.80 1280278.80
-1280278.80 -1280278.80 1280278.80 1280278.80
Stiffness Matrix for element 4:
It is same as the element 2 because of symmetry.
1280278.80 1280278.80 -1280278.80 -1280278.80
1280278.80 1280278.80 -1280278.80 -1280278.80
-1280278.80 -1280278.80 1280278.80 1280278.80
-1280278.80 -1280278.80 1280278.80 1280278.80
4

23. 21
Ansys 2D Calculation Results
Reactions
PRINT REACTION SOLUTIONS PER NODE
***** POST1 TOTAL REACTION SOLUTION LISTING *****
LOAD STEP= 1 SUBSTEP= 1
TIME= 1.0000 LOAD CASE= 0
THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM
NODE FX FY FZ
1 5.1650 5.1650 0.0000
5 -5.1650 5.1650 0.0000
TOTAL VALUES
VALUE 0.14211E-13 10.330 0.0000
Forces per element 2D modelling
PRINT FORC ELEMENT SOLUTION PER ELEMENT
***** POST1 ELEMENT NODE TOTAL FORCE LISTING *****
LOAD STEP= 1 SUBSTEP= 1
TIME= 1.0000 LOAD CASE= 0
THE FOLLOWING X,Y,Z FORCES ARE IN GLOBAL COORDINATES
ELEM= 1 FX FY FZ
1 -3.2046 -5.1650 0.0000
2 3.2046 5.1650 0.0000
ELEM= 2 FX FY FZ
2 3.2046 -5.1650 0.0000
3 -3.2046 5.1650 0.0000
ELEM= 3 FX FY FZ
3 3.2046 5.1650 0.0000
4 -3.2046 -5.1650 0.0000
ELEM= 4 FX FY FZ
4 -3.2046 5.1650 0.0000
5 3.2046 -5.1650 0.0000

24. 22
ELEM= 5 FX FY FZ
5 0.76532E-15 0.0000 0.0000
3 -0.76532E-15 0.0000 0.0000
ELEM= 6 FX FY FZ
3 -0.76532E-15 0.0000 0.0000
1 0.76532E-15 0.0000 0.0000
ELEM= 7 FX FY FZ
2 -6.4091 0.0000 0.0000
4 6.4091 0.0000 0.0000
All the Forces & Stress in 2D modelling
PRINT ELEMENT TABLE ITEMS PER ELEMENT
***** POST1 ELEMENT TABLE LISTING *****
STAT CURRENT CURRENT
ELEM FORCE STRESS
1 -6.0784 -158.29
2 6.0784 158.29
3 -0.56551 -14.727
4 -6.4091 -166.90
5 5.5657 144.94
6 -6.7435 -175.61
7 0.56551 14.727
MINIMUM VALUES
ELEM 6 6
VALUE -6.7435 -175.61
MAXIMUM VALUES
ELEM 2 2
VALUE 6.0784 158.29

25. 23
Test Day Results & Pictures:
Figure 23 Weight of the final bridge
Figure 24 Final bridge carrying 1 kg Load during final test

26. 24
Conclusion
It is clear that the results coincide with the hand calculations & the Ansys results obtained on 2D & 3D modelling.
 Ansys workbench has many modelling characteristics with which to model the paper straw bridge
 FEA can do the following:
Modelled paper straw bridge on inventor & meshing the model & deriving the results.
 Model’s accuracy was validated using FEA where all the boundary conditions were considered to be ideal.
 The development of the model on FEA illustrates not only the capability of Workbench and Mechanical ADPL of Ansys
but also represents the behavioral aspects on the realistic structure predicting the stress, deflection, strains while
ignoring the unnecessary complications.
The bridge was thoroughly design and tested to remove the flaws. The final bridge obtained after rigorous effort of these
results.

27. 25
References
Biggs, R. M. (2000). Finite Element Modelling & Analysis of Reinforced-Concrete Bridge Decks. Charlottesville, Virginia: Viriginia Transport
Research Council.
Chen, W. Y. (1993). Finite Element Analysis. International WorkShop in finite element modelling, 36-117.
Chowdhury, M. (1995). Further Considerations for Nonlinear Finite Anlysis . Journal of Structural Engineering, 1377-1379.
Graddy, J. B. (1995). Factors Affecting the design thickness of Bridge Slab. Austin: Center for Transportation, University of Texas.
Misch, P. (1998). Experimental and Anlytical Evaluation of an Aluminium Deck Bridge. Charlottesville: University of Virginia .
Razaqpur, A. (1990). Analytical Modelling of Nonlinear Behaviour of Composite Bridges. Journal of structural Engineering , 715-1733.

28. 26
Appendix
Mesh
Meshing refers to a geometrical representation of set of fine elements. This feature allows to split the whole design in a set of
The fine structures that analyse the stress and deformation to combine and produce a perfect set of results like the equivalent
Stress, strain or deformation of a part designed. Meshing plays an important role in the Finite Element Analysis (FEA) ANSYS to
Understand the part designed. It is an important and critical part of engineering. This feature provides the balance to the
Requirements and the right mesh in each simulation (ANSYS, 2014
Skweness
Skweness is primary used to determine the quality of the mesh. It usually determines how close the element to the ideal ones is.
Extremely high skewed elements are never acceptable in FEA analysis (Inc., 2014)
(Siemens, 2014)
Aspect ratio refers to the ratio of the longer side to the shorter side of the mesh, ie. L/b. It is acceptable to have 70% of the
Mesh with Aspect ratio < 4 & Element quality 70% of mesh > 0.8
First Design generation:

29. 27