Structural Analysis of Pylons, Columns and Carriage Elisa Buckner - Mehul Chauhan - Uliana Doro - Naman Gupta - Johannes Vogt -

Alexander Andfossen

Problem Statement and DefinitionHyperloop is a concept of a high-speed transportation system between Los Angeles and San Francisco. Some Features:

- Reduced pressure tubes- Pressurized capsules (ride on an air cushion)- Distance: 350 miles- Average speed: 600 mph (Top speed: 760 mph)

The goal of this group is a structural analysis of the pylons and carriage of the hyperloop with the finite element method. To achieve this goal the following steps have to be solved:

1. Determine geometry of tube and track. 2. Determine the load felt by the pylon/columns from the capsule and determine the boundary conditions. 3. Investigate the stresses and displacement on the pylon and tube from a stationary pod. 4. Investigate the stresses and displacement on the pylon and tube from the pod going over the tracks. 5. Investigate the stresses and displacement on the pylon and tube during an earthquake. 2

1. GeometryRestrictions:

- Provide enough space for two capsules in each direction- Provide connection between carriage columns and pylons

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Pylon:Height: 7mWidth - Bottom: 2mWidth - Top: 6.83mDepth: 1m

Tube:Inner Radius: 1.650mOuter Radius: 1.675mLength: 30m

2. Load calculation

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With a given geometry the boundary conditions can be setWe can consider static load of whole capsule 26000*9.81=255.060 KN

On considering the safety factor of 1.3 the designed load should be 255.06*1.3= 331KN

From tube geometry, column geometry and material of tube and column we can find out static load of tube on column.

Load will be from: Structural elements of the tube, pylons, foundations, girders, valves, airlocks, vacuum pumps, vacuum system and the carriage.

Vehicle Component Weight (kg)

Capsule Structure & Doors: 3500

Interior & Seats: 2700

Propulsion System: 800

Suspension & Air Bearings: 1300

Batteries, Motor & Coolant: 5500

Air Compressor: 2500

Emergency Braking: 800

Passengers & Luggage: 1400

Car & Cargo: 7500

Total/Capsule (kg): 26000

3. Material and Physics Used

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ThrustDrag

mg

Fn ● Pylon: concrete Yield Strength = 3 MPa (Tensile)

● Tube: structural steel Yield Strength = 250 MPa

● Thrust obtained from compressor power outputCompressor Output = 49MW

Force = 144kN (Power Unit Conversion)

● Drag = 320N (From Alpha Doc)

● Frictional Forces Negligible from Air Bearings

Direction of Movement

4. FEA Mesh Details

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Tube: square mesh

Pylon: triangular mesh

Total elements: 8063

Total nodes: 29946

Results:STATIC ANALYSIS

Boundary conditions: fixed at bottom, no displacement in the axial direction and y-direction at the ends of tubes, tube to tube modeled as bonded, tube to pylon modeled as frictional 0.2

Analysis: Three orientations analyzed: pod in whole length of tube, pod on either end of tube, pods occupying middle of tube.

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Results:TRANSIENT ANALYSIS

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● Total Deformation

Equivalent Stress(Von-mises)

Results:MODAL ANALYSIS

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● Used most-stressed state of two pods occupying middle of the tube.● The mode shape corresponding to frequency 10.58Hz has most deformation building up at pylons which is about 1.33mm.● Other significant deformation frequencies are 18.97Hz, 16.73Hz and these deformations are mostly on tubes.

Results:FATIGUE ANALYSIS

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Data is for the tubes only with a load of 510kN (twice the static load).

For steel, the S-N diagram becomes horizontal at some point. The strength at this point is called the endurance limit Se´ and occurs somewhere between 10^6 and 10^7 cycles.

Most steels have an endurance limit about half the tensile strength

Structural Steel > Tensile Yield Strength 250 MPa =>Endurance 125MPa

44 MPa Maximum value ( von-Mises) Stress.

If the applied stress level is below the endurance limit of the material, the structure is said to have an infinite life.

Endurance Limit Modifying Factors: surface conditions, size, loading, temperature, reliability, and other factors.

Endurance Limit (125 Mpa)

Interpretation, Discussion and Conclusion

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Static and Transient Analysis: Peak stresses did not exceed material yield strength, and deformation of approximately 2mm for static analysis. The tube length analyzed was 30m, and we considered the deformation minimal to this length.

Modal Analysis:The only desired modes were some of the low frequencies because they are the most prominent modes at which the structure will vibrate, dominating all the higher frequency modes.

Fatigue Analysis: Using the S-N curve for structural steel the stresses compared to our model were below the critical stress and our structure will not fail until 10^6 cycles with 2 times the load.

References

http://www.spacex.com/sites/spacex/files/hyperloop_alpha-20130812.pdf

http://www.computationalfluiddynamics.com.au/ansys-multiphysics-elon-musk-hyperloop

https://www.youtube.com/watch?v=haJD6gPZwGo

http://earthquake.usgs.gov/learn/facts.php

http://forums.thepaceline.net/showthread.php?t=148267&page=4http://www.ux.uis.no/~hirpa/KdB/ME/S-N%20diagram.pdf

Shigley’s Mechanical Engineering Design 12