Arch and vault - libvolume3.xyzlibvolume3.xyz/civil/btech/semester4/structural...Arch and vault structures Prof Schierle 2 Funicular vs. load Load type Funicular 1+2 Single point load

Arch and vault structures Prof Schierle 1

Arch and vault


Funicular vs. loadLoad type Funicular

1+2 Single point load Triangle

3+4 Two point loads Trapezoid

5+6 Uniform load Parabola

7+8 Mixed load Gothic curve

9+10 Self weight Catenary

11+12 Radial load Circular


Load and form 1 Polar polygon of parabolic cable 2 Parabolic funicular cable under uniform load 3 Polar polygon of parabolic funicular arch 4 Parabolic funicular arch under uniform load5 Polar polygon of asymmetrically loaded cable 6 Funicular cable under asymmetric load 7 Polar polygon of asymmetrically loaded arch8 Arch funicular under asymmetric load 9 Global moment of horizontal couple M = H d10 Arch bending due to funicular offset

M = F eF = arch forcee = arch offset from funicular line

11 Variable arch depth (optimal span/depth = 5)12 Arch force vs. arch depth (rise)

11 12


Arch hinges1 Fixed-end arch 2 Fixed-end arch bend under temperature change3 Fixed-end arch footing subject to overturn moment4 Fixed-end arch bend under uneven settlements 5 Two-hinge arch6 Two-hinge arch, bend under temperature variation 7 Two-hinge arch footing without overturn moment8 Two-hinge arch, bend under uneven settlements 9 Three-hinge arch 10 Three-hinge arch, free to move under temperature

change without secondary bending stress 11 Three-hinge arch foundation, with vertical and

horizontal loads 12 Three-hinge arch, free to move under uneven

settlement without secondary bending stress


Exhibit hall Klagenfurt, Austria (1966)Architect: O LoiderEngineer: Timber construction contractor

The 96x75m hall 3-hinge wood arches span 96 m

Arches of twin I-beam cross-sections, spaced 6.8 m,

are crescent-shaped to fit the funicular pressure line

for various loads to minimize bending stress.

1 Axon

2 Wind racing detail

3 Arch crescent profile

4 Arch cross-section

A Glue-lam twin arches, 2-16x100 to 187 cm

B Arch flanges, 16x41cm glue-lam

C Roof purlins, 8x22cm solid wood

D L-shaped purlins, 2 – 8x22cm, brace arches

E Wind bracing, 8x8 cm


Storage hall Walsum, GermanyEngineer: Bauabteilung BrüninghofThe circular hall of 94.6 m diameter is 20.8 m highEight radial 3-hinge glue-lam arches span 94.6 m A concrete tension ring/wall resists the lateral arch thrust Arches are crescent-shaped to fit the funicular pressureline for various loads to minimize bending stress. 1 Roof framing plan2 Cross-section 3 Hinge support4 Arch bracing detailA Glue-lam arch, 20x140-226 cm, crescent shapedB Glue-lam beams, 8-16/16-70 cm, based on spanC Arch bracing, 8x16cmD Steel hingeE Concrete tension ring


Wood arch design

Assume:Glue-lam arches, spaced 16’, three-hinged for easeof transportation and to avoid settlement stress.

Available dimensions: ¾”laminations;3 1/8”, 5 1/8”, 6 3/4”, 8 3/4”, 10 3/4” wide).

Based on case studies, use conservative allowable buckling stress: Fc’= 200 psi

Code live load of 20 psf, reduced 40% to 12 psffor tributary area > 600 sq. ft.

Loads:LL = 12 psfDL = 18 psf = 30 psf


Distributed loadw = 30 psf x16’/1000 w = 0.48 klfGlobal momentM = w L2/8 = 0.48 x 1002 / 8 M = 600 k’Horizontal reactionH = M/d = 600 / 20 H = 30 k Vertical reactionR= wL/2= 0.48x100/2 R = 24 kArch compression (max.)C= (H2+R2)1/2=(302+242)1/2 C = 38 kCross section areaA= C/Fc’= 38/0.2 ksi A = 190 in2

Glue-lam depth (try 51/8“ wide glue-lam)t =A/width =190/5.125= 37Use 50 boards of ¾” t = 37.5” Check slenderness ratioL/t= 100’x12”/37.5 L/t = 32, OK

C R

H


NoteArch slenderness L/t is usually about 30 to 40;hence 32 is OK; while the 5 1/8” arch width isbraced against buckling by roof diaphragm.

Graphic Method• Draw equilibrium vector at support.

starting with computed vertical reaction• Draw a line parallel to support tangent and a

horizontal line• Measure length of unknown vectors:

horizontal vector is horizontal reactionsloping vector is is max. arch force.


Wood arch details

1 Two-hinge arch

2 Three-hinge arch

3 Crown hinge concealed

4 Crown hinge exposed

5 Base hinge concealed

6 Base hinge exposed

7 Base moment joint concealed

8 Base moment joint exposed


Bus Station Chur, Switzerland (1992)Architect: Richard Brosi / Robert ObristEngineer: Toscano / Ove Arup (Peter Rice)

Located over a train station, the bus stationconnects ski resorts.The glass roof provides scenic mountain views.Inclined 16” steel arches span a 164’ platform.Radial strands resist lateral thrust and buckling.Arches are suspended from outrigger masts. Arch/strut triangles resist lateral load.


Assume:Arch span L = 50 m / 0,3048 L ~ 164’Arch rise d ~ 30’Arch spacing e = (7.5 m/2) / 0.3048 e = 12.3’Arch outside =406 mm / 25.4 ~ 16”Arch wall thickness t ~ ¼”Arch inside diameter i = 15.5”Allowable steel stress Fa =0.6x50 ksi Fa = 30 ksiAllowable strand stress Fa = 210/3 Fa = 70 ksLL = 1.6 kPa x 0.145x144 in2/ft2 LL = 33 psfDL (estimate) DL = 27 psf LL+DL = 60 psf

Uniform arch loadw = 60 psf x 12.3’ / 1000 w = 0.74 klfGlobal momentM = w L2/8 = 0.74 x 1642/8 M = 2488 k’Horizontal reactionH =M / d = 2488 / 30 H = 83 kVertical reactionR = w L /2 = 0.74 x 164 /2 R = 61 kMax arch compressionC = (H2 + R2)1/2 = (832 + 612)1/2 C = 103 k


Max arch compression (from last slide) C = 103 kCheck allowable buckling stressRadius of gyrationr = (2+ i2)1/2/4 = (162 + 152)1/2/4 r = 5.48”Unbraced length (between strands)KL = 1.1 x164 / 7 KL = 26’Slenderness ratioKL/r = 26’ x 12” / 5.48” KL/r = 57Allowable buckling stress (AISC table) Fa=23 ksiArch cross sectionA =(2 -i2)/4= (162 -15.52)/4 A = 12 in2

Max. arch stressfa= C/A= 103 / 12 fa = 8.6 ksiCheck fa≤ Fa 8.6<23, OKMax strand forceT ~ H = 83 T~ 83 kRequired metallic strand areaAm = T/Fa = 83 / 70 Am = 1.2 in2

Gross strand area (70% metallic)Ag = Am/07 = 1.2/0.7 Ag = 1.7 in2

Strand size = 2(A/)1/2 = 2(1.7/)1/2 = 1.47” Use 1 ½“A = r2 r2 =A/ = 2r =2(A/)1/2



1 Cylindrical vault2 Rib vault3 Inverted cylindrical vault 4 Folded vault5 Undulated vault 6 Corrugated vault

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Some vault compositions generatecross vaults with intersections thatprovide implied ribs for improvedbuckling resistance.


A Ferro-cement unitB Site-cast concrete ribC Skylight

Exposition hall, Turin (1947-49)Engineer: Pierre Luigi NerviThe 75/94 m concrete vault of prefab Ferro-cement unitsto resist buckling, are joined by site-cast concrete. The wire mesh ferro-cement units integrate natural lighting.


Garden Festival Hall, LiverpoolArchitect/Engineer: Ove Arup

This 78/62 m project was designed for a dual purpose: • Central focal point for the festival - and afterwards• Sports center with pool, a multipurpose hall

squash courts, a gymnasium, and related facilities

Structure:• Three-hinge truss arches, spaced 3m• provides the flexibility required for both programs• Steel pylons support gravity load and lateral thrust• The vault has translucent 2 cm polycarbonate panels• The round endings are glad with corrugated aluminum


Airship hanger, Orly airport, FranceEngineer: Eugène FreyssinetThe first of two hangers, build in 1915 was the firstreinforced concrete vault.Each vault spans 80m, is 300m long and 56m high.The parabolic cross-section fits the funicular pressureline for uniform load distributed horizontally.To resist buckling under unbalanced load, the vaultsConsist of ribs of required depth without great dead load.The 6 cm concrete ribs are 7.5 m wide, and varyin depth from 5.4 m at the base to 3 m on top.Skylights are integrated with the ribs.

Palace Ctesiphon (531 AD)The ancient Palce Ctesiphon (Mesopotamien plain) has a brick vault of 80 ft span (about 1/3 of Fryssinet’s vault). The vault cross section approximates the parabolicfunicular pressure line for minimal bending stress.


IBM traveling exhibitArchitect: Renzo PianoEngineer: Ove Arup/Peter Rice

The design objective for this travelingexhibit pavilion was light weight andease of assembly and disassembly.The 10x50 m pavilion was on exhibit inmajor European cities.• Translucent polycarbonate pyramids

for natural daylight are supported bytwo sets of glue-lam arches on theinside and outside

• Aluminum joints link arch segments• The three-hinge vault allows thermal

change without secondary stress• A base platform adjusts for local sites


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Architect: Camelot Maily ZehrfussEngineer: Nicholas Esquillan

Alternate design by Nervi

Architect: Minoru Yamasaki;Engineer: Roberts & Schaefer


Design great arches

Arch and vault - libvolume3.xyzlibvolume3.xyz/civil/btech/semester4/structural...Arch and vault structures Prof Schierle 2 Funicular vs. load Load type Funicular 1+2 Single point load

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