(part1/2)collapse of the hyatt regency walkways 1981
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Mechanics of Materials
(CASE STUDY)
Investigation & Analysis for the
Collapse of the Kansas City Hyatt Regency Walkways (1981)
Group Members (ME-05 B)
Ali Faizan Wattoo NUST201305057BSMME
Farhan Ellahi NUST201304475BSMME
Muhammad Umair Qazi NUST201305329BSMME
Gohar Shoukat NUST201305490BSMME
Usama Zaid Malik NUST201304802BSMME
Submitted to
Dr. Irfan-Ul-Haq
Dr. Amir Mubashir
Page # 1
CONTENTS
1) ABSTRACT ------------------------------------------------------------------------ 2
2) INTRODUCTION ----------------------------------------------------------------- 2
3) ANALYSIS & RESEARCH -------------------------------------------------------- 3 3.1- Theoretical Analysis 3
3.1.1 Given Data and Assumptions
3.1.2 Tensile stress in Hanger Rods
3.1.3 Transverse Shear Stress in Box Beam
3.1.4 Bending stress in Box beam
3.1.5 Bearing Stress on Nut Cross-section
3.1.6 Bearing Stress on Washer Cross-section
3.1.7 Welded Area Strength
3.2 Conclusion drawn from theoretical analysis 9
4) RESULTS & FINDINGS ----------------------------------------------------------- 10
5) DISCUSSION & CONCLUSION -------------------------------------------------- 10
6) FUTURE PROSPECTS ------------------------------------------------------------------ 11
7) REFRENCES ------------------------------------------------------------------------- 11
* APPENDIX (Attached with the report)
Finite Element Analsis of the walkway structure on SolidWorks
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5
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1-ABSTRACT
In this research, an investigation of the collapse of two walkways in the Hyatt Regency Hotel
Kansas City (1981) has been carried out. The proposed design of the engineers was altered by
the fabricators due to the unavailability of required length of the rod. They replaced the single
long rod with two individual ones due to which there was a design load variation in the
supporting rods. After careful theoretical and mathematical analysis of the original design and
the fabricated design we found that the force distribution in one of the rods was doubled which
resulted in the failure of the beam-rod joint. We also found the original design also lacked
perfection. These findings were validated by simulating the original and the fabricated designs
through finite element analysis (FEA) on Solidworks. This report covers all the investigation and
analysis for both the designs.
2-INTRODUCTION
On July 17, 1981, during a dance party, the collapse of two walkways in the Hyatt Regency Hotel
in Kansas City resulted in the deaths of 114 human lives with a loss of millions of dollars. It was
one of the worst structural engineering failures in the history of United States.
The Hotel had lavish walkways connecting the two sides of the second floor and the fourth floor
which were designed by Jack D. Gillum and Associates, a structural design firm. Their original
proposed design consisted of a single continuous rod supporting both the walkways tying them
up to the roof truss. Due to difficulty in fabricating and setting up the single continuous rod the
fabricators altered the design for easy construction without being warned by the designers.
They replaced the one long rod with two individual shorter ones.
Investigations and forensic reports found the alteration in the original design as the major
cause of the incident. The engineering firm which proposed the design was held responsible. It
was supposed to point out the flaws and should’ve noticed the design alteration by the
fabricator. As a result the principal structural engineers lost their Missouri engineer’s licenses,
and the firm, Jack D.Gillum and Associates got dissolved.
This report covers the mathematical and structural analysis for both the designs to point out
the reason for this structural failure that consumed 114 precious lives.
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3-ANALYSIS & RESEARCH
3.1 THEORETICAL ANALYSIS
Here we will analyze the stresses produced as a result of redesign in hanging rod, nuts, beam
and welded area near the hanger rod and compare them with the allowable stresses to find out
the cause of failure.
For this we will proceed as follows:
3.1.1 Given Data and Assumptions
Pressure 90 kN
Material of beam A36 steel
Yield strength of A36 steel 250 MPa
Ultimate Tensile Strength of A36 steel 400 MPa
Shear Yield Strength of A36 Steel 0.5 × Sut = .5 × 400 = 200 MPa
Material of Bolts and Nuts A325
Yield strength of A325 234 MPa
Electrode used in weldings 620MPa
Ultimate Tensile Strength of A325 E60xx
Yield strength of E60xx 345 MPa
Ultimate Tensile Strength of E60xx 427MPa
Length of weld 2340mm
Type of weld between two C section Beams to
form a bonded Box Beam
Butt Welding
Page # 4
Standard Specifications of C Beams (MC8x8.5)
Load supported by hanger rod = 2P = 180 kN as shown in figure below:
We will consider the cross-section of hanger rod to be 1¼ in. in diameter.
Assuming the same thread sizes for nuts and washers; using ANSI standards:
Max. Nut Width across Flat = bn = 2 in.
Max. Washer diameter = 3 in.
Page # 5
3.1.2 Tensile stress in Hanger Rods
To calculate the tensile stress in the hanger rods consider following calculations:
A = 𝜋𝑑2
4 =
𝜋(1.25×0.0254)2
4 = 7.917 X 10-4 m2
σ= 𝑃
𝐴 =
180000
7.917×10−4 = 226 MPa < 234MPa
As it is less than the tensile strength of A36 steel so the stress in hanger rods is satisfactory.
3.1.3 Transverse Shear Stress in Box Beam
To calculate the shear stress in the box beam consider the following calculations:
𝐼 =2
12(95 × 10−3 × (7.9 × 10−3)3 + 2(. 095 × .0079) ×. 10552 +
2
12(. 00455 ×. 18743)
= 2.17 × 10−5 𝑚4
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𝑄𝑚𝑖𝑑−𝑝𝑜𝑖𝑛𝑡 = 𝛴𝑦′𝐴 = 2 × .04685 × .00455 × .09370 + .095 × .00790 × .09765
= 1.13 × 10−4 𝑚3
𝜏 =𝑉𝑄
𝐼𝑡=
180000 × 1.13 × 10−4
2.17 × 10−5 × (.00455 × 2)= 103𝑀𝑃𝑎 ≪ 200𝑀𝑃𝑎
Where
V : Shear Force
Q : Static Area above the axis about which we measure the thickness of the cross-section
I : Moment of Inertia about the Neutral Axis
t : Thickness
3.1.4 Bending stress in Box beam:
We will now be taking a look at bending moment in the box – beam. We have the following
cross-section.
A free body diagram of a section of the beam is as follows.
Maximum shear force will 180 kN, anyplace between the two opposing forces.
Maximum bending moment will lie infinitely close to the 90kN force, with magnitude
M =180,000 x 0.1 = 18,000 Nm
For cross section properties:
w = 9.5 cm = 0.095 m
d = 20 cm = 0.200 m
Maximum radius (at the corners) = 0.100 𝑚
Bending stress = 𝜎 = 𝑀𝑐
𝐼=
18,000 ×0.100
2.17×10−5 = 82.9 𝑀𝑃𝑎 ≪ 250 𝑀𝑃𝑎
This is much less than the yield strength of the material, so it is safe.
180 kN
90 kN
0.100 m
Page # 7
3.1.5 Bearing Stress on Nut Cross-section:
In the redesign of walkway supports, the nut and washers on the fourth floor walkway beam
supports double the load as compared to original design i.e.
F = 90 kN X 2 = 180 kN
Cross-sectional Area of Nut = A = 3√3𝑠2
2 -
𝜋𝑑2
4
Where, s = 𝑏𝑛
√3 =
2
√3
d = 1¼ in.
Thus we get:
A = 2.237 in2 = 2.237 x 0.02542 m2
A = 1.443 x 10-3 m2
σb = 𝐹
𝐴 =
180000
1.44×10−3 = 125 MPa < 234 MPa
This value is less than the tensile strength of A325 steel so value of stress is satisfactory.
3.1.6 Bearing Stress on Washer Cross-section:
To calculate the bearing stress on washer cross-section consider following calculations:
Here F = 180 kN
Cross-sectional area of washer = A = 𝜋
4(𝑑2
2 − 𝑑12) =
𝜋
4(32 − 1.252)
= 5.84 in2 = 3.77 x 10-3 m2
Bearing Stress σb on washer cross section = 𝐹
𝐴 =
180000
3.77×10−3 = 47.74 MPa
This value is considerably less than the tensile strength of A325 steel so stress on
washer didn’t cause failure.
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3.1.7 Welded Area Strength:
The load supported by nut and washer is acting on the welds as a reaction i.e.F = 180 kN
We consider that butt welds were used to join the two MC 8x8.5 beams to form box beams.
As discussed above:
Max. Nut Width across Flat = 2 in.
Max. Washer diameter = 3 in.
Since, the weld extends to about 2300mm, it is a very long welded region, and the force is
localized, its immediate affects will also be localized. By Saint Venant's Principle we assume any
localized effects of a localized force to be contained within 2-3 times the thickness ‘t’ of the
beam", so that makes, 2.5 x .3 = 0.75 in.
This distance is measured from the ends of the nut, which has a diameter of 2 inch, so in total,
it makes a distance of: 2 + 2 (0.75) = 3.5. So,
Effective weld length L = 3.5 in.
For MC 8x8.5 box beam of A-36 steel material,
We find out its toe thickness to be t = 0.311 in.
Thus taking effective weld throat to be equal to toe
thickness i.e.
h = 0.311 in.
Butt weld area under consideration:
A = h x l
=3.5 in. x 0.311 in
=1.0885 in2
=1.0885 x (0.0254 m) 2 = 7.023 x 10-4 m2
For butt weld, shear stress is given by following equation:
τ = 𝐹
ℎ𝑙
= 180 𝑘𝑁
7.023 𝑥 10−4
= 180000
7.023 𝑥 10−4
τ = 256.3 MPa
Page # 9
For butt weld, the allowable shear stress is given by:
τall = 0.30 Sut
Taking E60XX to be the electrode material:
Sut = 427 MPa
So τall = 0.30 (427)
= 128.1MPa
Thus, the shear stress acting is appreciably greater than allowable shear stress. Hence, it is
concluded that failure occurred due to the breaking of welds in the vicinity of nuts
and washers where the hanger rods were bolted.
It is to be noted that these values are calculated on maximum constraints. When we use 90
kN force (which is the case of single hanger rod), the stress comes out to be 128.1 MPa on
same maximum constraints. This value is equal to the allowable stress. But if the weld
length and throat are less than considered say:
l = 3.25 in.
h = 0.25 in.
So, τ comes out to be 171.69 MPa for 90 kN force i.e. it exceeds the limit.
Hence, the original design can also not be considered safe.
*See appendices for complete Finite Element Analysis (FEA) of the walkway structure
3.2 Conclusion drawn from theoretical analysis
- Hanger Rods bent Under the Impact of Fall
A = 5.24 x 10-4
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4-RESULTS & FINDINGS
From the above Analysis of the walkway structure, we found following results:
The Box beam fabricated by welding two C Beams, proves to be stable under Transverse, Bending and Normal Stresses.
Forces exceed their design load only on the contact surface between the nut of the hanger rod and the Box Beam.
The load applicable on the contact area becomes twice the maximum design load.
Structural analysis of the entire beam indicates failure at the joint of the top floor.
The weld is ripped apart by the shearing force induced by the nut of the hanger rod.
Weld Metal strength was unsatisfactory.
This increases the Bearing Stress causing the Beam to bend at its welded edges
producing plastic deformation and the nut to go through it.
The original design too was marginally safe.
The factor of safety for the weld group was equal to 1.
5-DISCUSSION & CONCLUSION
The structural analysis was conducted using Simplistic theory of Mechanics of Materials and
verified by Finite Element Analysis conducted on SolidWorks. Both the methods indicated that
the joint connecting the beam and the hanger rod was the failing point. However, weak joint
was not the cause of failure. The new design induced shearing forces and moments which
caused the loading on the top floor to almost double. The structure with a factor of safety
marginally over 1 could not withstand any further loading which triggered its collapse.
The sequence of events as indicated by the debris assessment could be that the weld failure
created a gap between the two C beams. This caused a reduction in area in contact with the nut
which increased the bearing stress several folds. Support structures must transfer their loading
to the ground instead of other critical members of the structure. When the member is
experiencing maximum design load, any further load or moment transmitted to it from
members shedding their load on it will cause it to exceed the design load and hence, fail.
Another important aspect mentioned by the report is the miscommunication between the
designers and constructors and the lack of quality control. Clearly, this episode only further
enhances the importance of a well-coordinated and controlled engineering approach.
Page # 11
A better design would have been to use Columns or Pillars as support structures instead of
hanging rods. Failure under compressive loading is unlikely compared to tensile loading.
The essential problem was a lack of proper communication between
the design engineers (Jack D. Gillum and Associates) and the manufacturers (Havens Steel).
6-FUTURE PROSPECTS
Transverse Shear Stress and Bending Stress Distribution Mapping over the Box Beam
cross Section.
Making assumptions more realistic.
Increase Accuracy of FEA of model by improving boundary conditions.
Fatigue Analysis to observe the affect of fatigue on the bridge.
Detailed alternative design proposal with Mathematical Reasoning and FEA for analysis.
Due to Limited number of pages, for further analysis and discussions, please refer to the
Appendix added.
7-REFERENCES
1. MECHANICS OF MATERIALS R. C. HIBBELER 9th EDITION, Publisher: Pearson Prentice Hall
(2014c)
2. *Marshall, Richard Detal. (May 1982). Investigation of the Kansas City Hyatt Regency
walkways collapse. Building Science Series 143. U.S. Dept. of Commerce, National Bureau of
Standards. Retrieved 2012-03-13
3. National Bureau of Standards (May 1982). "Investigation of the Kansas City Hyatt
Regency Walkways Collapse" (PDF). US Department of Commerce. Retrieved 2011-
01-26.
.
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THE END