Structural Engineering Art and Approximation

A Talk By

Hugh Morrison

Any Questions?

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And turn off mobile phones….

Summary of Talk

‘Why’ and ‘How’ the book came to be written

Illustration: Historic and Contemporary structure.

Samples from the book

Conclusion: the benefits of sketching and approximation.

Desert Island Engineering?I’m an engineer

get me out of here!

‘WHY’ and ‘HOW’ the book came to be written

TedsRamSTAADGSANO COMPUTER

P R O P O S E a n d T E S T O P T I O N S : s ke t c h e s a n d r o u g h c a l c u l a t i o n s

DESIGN is finding a solution within acceptable limits

APPROXIMATION

“ENGINEERING IS THE ART OF APPROXIMATION”

ART

C R E AT I V E T H O U G H T

a n d s e l f - e x p r e s s i o n

C u l m i n a t i n g i n a ‘ w h o l e s o m e ’ , ‘ p l e a s i n g ’ s o l u t i o n

Ove Arup Quote

Engineering problems are under-defined,

there are many solutions, good, bad and indifferent. The art is to arrive at a good solution.

This is a creative activity, involving imagination, intuition and deliberate choice.”

SUMMARYWith simplified methods one can be assured that:

THE PROBLEM IS DEFINED

THE ASSUMPTIONS ARE CLEAR

THERE IS A ROUGH SOLUTION

ONE KNOWS APPROXIMATELY HOW THE STRUCTURE WILL BEHAVE

THE COMPUTER MODEL IS VERIFIABLE

One thing to be sure,I will not be presenting anything like this…

A REVIEW OF AN HISTORIC AND A CONTEMPORARY STRUCTURE

GOOD EXERCISE: Look at Built Structures

UNFAMILIAR STRUCTURES: To avoid preconceptions

SKETCHES

APPROXIMATE CALCULATIONS

ASSUMPTIONS LISTED

R100 AIRSHIP

Chief designer: Barnes Wallis

Lead Stress Engineer: Neville Norway Shute

DESCRIPTION OF STRUCTURE

Duralumin transverse and longitudinal frames

Trussed approx. 680mm deep

16 side polygon with steel

radial ties – circa. 25-35mm dia.

Circa 15 transverse frames at 13.5m (45ft)

Hydrogen filled buoyancy

bags top centre.

Powered by 3

diesel gondolas

Transverse Frames

Transverse FrameMax 40m diameter

Maximum net pressureAssumed 1kPa

ASSUMPTIONS

UNIFORM SUCTION: RING INEFFECTIVERadial Cables Resist Load

UNIFORM INWARDS PRESSURE: RADIAL CABLES INEFFECTIVERing Resists Load

ASYMMETRICAL LOADING: (SUCTION AREA) CABLES IN TENSIONRING IS INEFFECTIVE IN BENDING

HAND CALCULATIONS IN EASY STEPS

CONSTANT SUCTION 1kPa CONSTANT PRESSURE 1kPa UNEQUAL PRESSURE 1kPa

R100 CONCLUSION

STAGE 2: MORE DETAILED DESIGN CHECKS

Check Ring with combined bending/cable tension. Computer analysis of a 2D half frame linear/non-linear

Cable stress close to yield – examine further 35m diameter?

Buckling checks?Longitudonal Frame checks?

LEVEL OF REFINEMENT: DECIDE WHAT IS APPROPRIATE?

FOR EXAMPLE:

NEVILLE SHUTE: A Delighted Engineer...

After literally months of labour, having filled perhaps fifty foolscap sheets with closely pencilled figures, after many disappointments and heartaches, the truth stood revealed, real, and perfect, and unquestionable; the very truth.”

ISTRUCTE STAIR HQ BASTWICK STREET

Expedition Engineers

Hugh Broughton Architects

June/July 2015: Design FeatureIstructE magazine

REVIEW OF DESIGN: alternative load path CONSIDERED

ISTRUCTE STAIR BASTWICK STREET

Traditional Cantilever Stair – Load path

Torsion Increases down the stair

Tread loads accumulate

Torsion and Shear resisted By wall

No cantilever bending

ASSUMPTIONS

1. GLASS balustrade ineffective

4. 50% STAIR and balustrade load cumulatively onto outer stringer

3. 50% STAIR loaded onto wall

5. LOCAL TORSION resisted at each tread by STRINGER DOES NOT ACCUMULATE

2. BARS transfer shears/torsion into wall

6. LANDING supports upper half of FLIGHT

FREE BODY DIAGRAM

Balustrade/stringer/half tread each 1kN

Local applied Torsion (over tread width)= (10-9)x0.25 = 0.25kNm

Resolving Shears at support

R1= T/0.08m+0.8/2=3.6kN (down)

R2=-T/0.08m+0.8/2=-2.7kN(up)

Cumulating loads onto stringer/landing x10 treads max = 10kN

Alternative Load Path

1OkN

INITIAL MODEL - VERIFICATION

Concrete treads 40mm thick (plates)

REACTIONS +3.7/2.8 – OK

STRINGER AXIAL FORCE 10.6kN – OK

‘LIKE WOBBLY TEETH’ – WALL SUPPORTS with VERY LOW PULL OUT STIFFNESS

75x30mm stepped stringer (steel)

INITIAL MODEL DEFLECTIONS

DEFLECTIONS HIGH NO GLASS – 10mm ADDING GLASS – DEFLECTION 0.50mm

REVISED MODEL – FIXED SUPPORTSBy fixing supports shears at support model corresponded to Expedition design

EXPEDITION MODELHORIZONTAL SHEARS

EXPEDITION MODELNO GLASS –DEFLECTION 1mm

EXPEDITION MODEL14.9Hz

REVISED MODEL – NATURAL FREQUENCY

Natural Frequency at 14.9Hz similar to Expedition site observations

DOES THE ALTERNATIVE LOAD PATH MODEL HELP?

SINCE GLASS BALUSTRADE INCLUDED – natural frequency > 14.9Hz

POST DRILLED ANCHORS POSSIBLE (pre-forming holes complicated construction)

CONCLUSION

Sketches and hand calculations used to understand problem

Support loads may be estimated

Elements may be Initially Sized and Checked

Initial COMPUTER MODEL built from FIRST APPROXIMATIONS

EXAMPLES FROM THE BOOKStructural Engineering: Efficacy, Balance and Grace

Simply Supported Beams

Cantilever Beams

Continuous Beams

Framed Structures

Trusses and Vierendeel Structures

Tension and Suspension Structures

Arches, Vaults and Domes

Torsion Structures and Ring Beams

Plate Structures

Deep Beams, Load Carrying Walls and Diaphragms

Dynamics

Learning from Failure

TRIANGULAR LOADING – ASSUMING UDL 2/3 PEAK

Classic Bending Moments/Shears UDL in place of Triangular Loading

Equivalent UDL 2/3 peak

+33% Bending

+0% max shear

+33% deflection

ASSUMING CENTRAL POINT LOAD – WHEN ACTUAL LOAD OFF CENTRE

Classic Bending Moments/Shears Use When Point Load off-centre (up to Middle Third Zone)

Equivalent Assume Central Point Load

+11% Bending

-140% max shear – calculate separately!

+15% deflection

CANTILEVERS

Comparison of Cantilever with Simply Supported

Cantilever with BackspanPoint Load

Increasing backspanTo 4L 4xencastre

Cantilever with BackspanUDL

Increasing backspanUDL backspan increased influence

FRAME STRUCTURES

Wind Frame TraditionalDesign

Wind Loading – Virtual Pins Columns

Design Beams Assuming Simply Supported

Quick estimation of Wind Bending

TRUSSES AND VIERENDEELS – KING POST TRUSSKingpost Truss

Statically Indeterminate

Combination of Beam and Truss Action

TENSION STRUCTURES – FABRIC TENSION ROOF STRUCTURE

Goodwood Racecourse - 1991

NON LINEAR ANALYSIS

Form Finding (dynamic relaxation)

LINEAR ESTIMATION POSSIBLE

Assume line load inFabric (say 3kN/m)

Cable loads from T=PR(utilise railway curves)

External reactions from collected cable loads

TENSION STRUCTURES – FABRIC TENSION ROOF STRUCTURE

Internal Force Diagram

External Forces Net Effect on Supporting Structure

COMPRESSION - CATHEDRAL BUTTRESSING – THE MIDDLE THIRD RULE!

Cathedral Section

Check Foundation thrust-line in middle third

Estimate Buttress (and Pinnacle) weight

Simple thrust from vaulted roof

Geometric check– resolved buttress counterweight

DEEP BEAMSQuick Check Table

Reinforcement Estimate

Lever Arm 0.62d

Check Shear overall rectangular section

Or resolve by STRUT-TIE model

DYNAMICS – DISCOMFORT/PERCEPTION ASSESSMENT

Fundamental Natural Frequencies – tendency for slender structures to resonance

Summary of terms

Fundamental Frequencies

Damping Ratios

Simple Excitation Calculations

Discomfort Criteria

Lateral Frequencies Tall Buildings

FOOTBRIDGE/RAMP 10m SPAN

Actual 10m span structure with screed floor fn 2.6Hz

NATURAL FREQUENCY 2.6Hz. Resonance – LIVELY!

GLASS BALUSTRADE DAMPING

STADIUM CANTILEVER TIER RESPONSE

CALCULATION based DYNAMIC MAGNIFICATION

Response Chart Simplified

STADIUM tier 3.5Hz NATURAL FREQUENCY

Check further < 6 Hz

EXERCISE BOOK

A POCKET COMPANION

FOLLOWS DESIGN PROCESS

15 EXERCISES RELATED TO REALISTIC PROBLEMS

CROSS REFERS TO MAIN BOOK

WHAT NO SPREAD?!

AND FINALLY…STRUCTURAL CURIOSITIES….

STABLE?

THE TALK…..

‘Why’ and ‘How’ the book came to be written

Illustration: Historic and Contemporary structure.

Samples from the book

Conclusion: the benefits of sketching and approximation.

THANK YOU

ANY QUESTIONS?