یوجبشنادروگتاهراوهگزbayanbox.ir/view/1696346280284382007/Plates-07-Shells-01-Membrane-to... ·...
Transcript of یوجبشنادروگتاهراوهگزbayanbox.ir/view/1696346280284382007/Plates-07-Shells-01-Membrane-to... ·...
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ز گهواره ات گور دانش بجوی (ص)حضرت ایپمبر اکرم
دانشکده فنی و مهندسی گروه مهندسی عمران
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تنش های غشائی در پوسته ها
(Membrane Stresses in Shells)
فصل هفتم
دورانی های پوسته غشایی نیروی عمومی معادالت -1
مرکزی متقارن بار اثر تحت دورانی های پوسته -2
متقارن شکل تغییر -3
نامتقارن بار تحت دورانی های پوسته -4
کلی شکل با ای استوانه های پوسته -5
(Contents)فهرست مطالب
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مقدمه
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Stadium in Jeddah
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Barrel Shells, Oakland Airport
Reinforced Concrete Roofs
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Rennbahn Madrid - Torroja 1935 - abgespannte Wellenschale mit ca. 13 m Kraglänge
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Palazetto dello Sport in Rom - Nervi 1958-60
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• BP-Tankstelle Autobahn Bern – Zürich Schweiz
Toronto Sky Dome
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Montreal Olympic Stadium
Stadionüberdachung
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سازه ورزشگاه
ورزشگاه اودام
تحلیل نیروها و تغییر
شکل سازه
معرفی سازه
3تصویر
2تصویر
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سیستم های چادری سیستم های چادری با پایه ها و نقاط اتصال متناوب
سیستم هایی باا قااااگار یااااگی شااایانی نقااااط اتصال
سیستم های چادری نمونه اجگا شده
استادیوم المپیک مونیخ
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Early branch development of domes
Hemispherical dome (Haghia Sophia, Turkey, 6th century)
Pointed dome (Tomb of Atreus, Greece, 1325 B.C.)
Catenary dome (Ctesiphon, Iraq, 6th century)
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Forces in Arches and Vaults
HT = Horizontal thrust LT = Line of thrust which represents the successive action of the voussoirs W = Vertical weight of the masonry and overload (dead and live) T = Thrust, resultant force of the horizontal thrust and weight
Forces in Arches and Vaults
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Imam Dome, in Isfahan (1612-38 (A.D.)
Imam Dome, in Isfahan (1612-38 (A.D.)
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:فرضيات
1 .است كوچك پوسته ميان انحناي شعاع به پوسته ضخامت نسبت-1Rt
.است كوچك پوسته ضخامت با مقایسه در ها مكان تغيير انداره-2
Z .باشد مي كردن صرفنظر قابل نيز اندازه-4
تئوری پوسته های نازک(Theory of Thin Shells)
0~,0 ZxZyZ
بر عمود و صفحه صورت به شكل تغيير از بعد پوسته ميان بر عمود صفحات-3 .مانند مي باقي پوسته ميان
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غشایی نيروهای سيستم
(Membrane Forces)
خمشی نيروهای سيستم
(Bending Forces)
تنش های غشائی(Membrane Stresses)
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عمل مقاومت در مقابل بار یک پوسته(Load Resistance Action of a Shell)
t= 0.4 mm ضخامت
و دست، فشار توسط مرغ تخم سخت شکستن مثال قاشق ضربه توسط مرغ تخم راحت شکستن
t/r=0.4/20=1/50=0.02 بنابراین
در یک تخم مرغ، r= 20 mm دوران محور حول انحناء شعاع
دست فشار توسط مرغ تخم سخت شکستن مثال قاشق ضربه توسط مرغ تخم راحت شکست و
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محور دوران
منحنی مداری
منحنی نصف النهاری
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محور دوران
منحنی مداری
منحنی نصف النهاری
(Meridional Angle) النهاری نصف زاویه = (Parallel Angle) مداری زاویه =
r1 = ضلع به مربوط النهاری نصف شعاع CD (محور بیرون آن مرکز (است واقع دوران
r2 = ضلع به مربوط مداری شعاع AC (واقع دوران محور روی آن مرکز (است
((طول واحد بر) مداری نیروی = (Parallel (Hoop) Force)
محور دوران
منحنی مداری
منحنی نصف النهاری
واحد بر) النهاری نصف نیروی = (Meridional Force) (طول
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Basic Structural Principles
Shells
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Basic Structural Principles
Forces in Arches and Vaults
HT = Horizontal thrust LT = Line of thrust which represents the successive action of the voussoirs W = Vertical weight of the masonry and overload (dead and live) T = Thrust, resultant force of the horizontal thrust and weight
Basic Structural Principles
Forces in Arches and Vaults
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Basic Structural Principles
Forces in Arches and Vaults
Structural Systems of Domes
• Single-Shell Domes
• Double-Shell Domes
• Triple-Shell Domes
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Single-Shell Domes
Double-Shell Domes
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Double-Shell Domes
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• Imam Dome, in Isfahan (1612-38 (A.D.)
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Triple-Shell Domes
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Iranian Arches
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•
•
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•
•
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•
•
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Brick Arrangment
Annular Course
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_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
شکل گنبد های بنایی بدون ممان و بدون کشش(The Shape of Momentless Tensionless Masonry Domes)
What Is the Shape of the Meridional
Curve and Thickness Variation of
Masonry Domes without Tensile
Stresses and Bending Moments?
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
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_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
1cos)( rrprNrNd
d
rpr
N
r
N
21
* Equilibrium Equations for Symmetrically
Loaded Shells of Revolution:
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
* By Eliminating in Regions where It
May Become Tensile, That Is : N
0N
\1
0rhh
Bph
Ar
cos
sin1ln
22
Thickness
Radius
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In Taj-al-Mulk dome (1088 A.D.) with its striking
geometry, containing the Golden Ratio and Golden Mean spiral:
* For weight loading the dimensions of the dome exactly
match the mathematical formulae for the shape of the
meridional curve and thickness variation of masonry
domes without tensile stresses and bending forces.
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
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وزن بار تحت الملک تاج گنبد در النهاری نصف های تنش (مربع متر بر نیوتن 500000 = فشاری مقاومت)
وزن بار تحت الملک تاج گنبد در مداری های تنش (مربع متر بر نیوتن 50000 = کششی مقاومت )
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_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
* The resultant stresses due to the system of bending
forces are negligible compared with the system of
membrane forces not only for weight load but also
for wind and temperature and more significantly
for the dynamic effects of earthquakes.
Taj-al-Mulk Dome
Taj-al-Mulk dome, variations of forces along the
height at the critical section _____________________________________________________________________ Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
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Taj-al-Mulk dome, variations of bending
moments along the height at the critical section. _____________________________________________________________________ Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
Taj-al-Mulk Dome
Taj-al-Mulk Dome, Mode Shapes
Hz803.371 f
f2 47 427 . Hz
_____________________________________________________________________ Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
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f3 55182 . Hz
Hz574 f
____________________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
Taj-al-Mulk Dome, Mode Shapes
f5 63833 . Hz_____________________________________________________________________ Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
Taj-al-Mulk Dome, Mode Shapes
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* Is Very Small.
* Is Negligible.
* Natural Frequencies: 37.8,
47.4, 55.2, 57 and 63.8 Hz
M
M
_____________________________________________________________________ Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
Taj-al-Mulk Dome
Stresses in the Taj-al-Mulk Dome at the Critical Section
____________________________________________________________________ Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
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_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
* The resultant stresses due to the system of bending
forces are negligible compared with the system of
membrane forces not only for weight load but also
for wind and temperature and more significantly
for the dynamic effects of earthquakes.
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
Taj-al-Mulk Dome
* FE Analysis Shows:
Different Shapes of Cross-Section, or
Meridional Thickness Variation
Would Increase the Magnitude of
Internal Stresses and Forces.
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* Persian architecture is the Sacred
Geometrisation of Divine Beauty.
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
* Persian architecture is the Sacred
Geometrisation of Divine Beauty.
_____________________________________________________________________
Mehrdad Hejazi, Dept. of Civil Engg., Faculty of Engg., Univ. of Isfahan, Isfahan, Iran
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مثالبر واحد سطح را pسقف گنبدی کروی شکل زیر تحت بار وزن
:مطلوبست. در نظر بگیرید .نیم کرویتعیین تنش ها برای یک گنبد –الف
صورتی در گنبد این برای کششی و فشاری های تنش کنترل -ب قطر و cm 20 ضخامت دارای و شده ساخته آجری مصالح از کهm 26 باشد.
.گنبد موضعی کمانش کنترل -ج
The Golden Ratio * It is often designated by the Greek letter Φ, for
Phideas (circa 490-430 B.C.), Athenian sculptor and artistic director of the construction of the Parthenon, who supposedly used the Golden Ratio in his work.
* Found in fundamental forms: plants, flowers,
viruses, DNA, shells, planets and galaxies.
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* The Golden Ratio is the unique ratio of two terms when the ratio of the larger term to the smaller term is in the same way as the smaller plus larger to the larger.
= (1+√5)/2 = 1.618
longer = shorter = 1
Sum = 2
* The Golden Ration symbolises the regeneration and progression and extension from the Unity as each generation is linked to its ancestors. It is the perfect division of the Unity.
* The Golden Ratio is the most pleasing aesthetic proportion.
*
*
....)))))../11/(11/(11/(11/(11/(11 432322 ;;1;1/1
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1AB
1 FBEG
)618.1(EB, )618.0(11 GB
,
)382.0(11 FGGI
,
)382.0(1 2FG
,
)236.0(1 3JG
The Golden Ratio in the pentagon and pentagram
Human canon and the Golden Ratio.
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The Fibonacci Series in the chronology of rabbit populations.
The Fibonacci Series in the distribution of leaves around a central stem: 3 leaves in 5 turns, 5
leaves in 8 turns.
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* The Divine Ratio as sacred measure
and aesthetic proportion in order to
embody the spirit in the matter.
* Greeks sought divinity at the Oracle of
Del-Phi.
* Pythagoras was initiated in Egypt’s
Mystery School temples in the ancient
city of Phi-la-del-Phi-a.
The Great Pyramid and the Golden Ratio.
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Parthenon, the Golden Rectangle.
1
Spirals
* The spiral created by a recursive nest of
Golden Rectangles found in:
** In snake coil
** In an elephant trunk
** In the cochlea of the inner ear
** In the shape of the Nautilus
pompilius shell
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Nautilus pompilius, the Golden Mean spiral.
Seed distribution in sunflower and pinecone based on the Golden Spiral.
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* For the Pythagoreans this form symbolises
the dynamics of the rhythmic generation of
the cosmos, and represents universal love.
* In Persian architecture, arabesque patterns
are based on ascending spirals with
succession of form elements indicating the
idea of infinity and multiplicity, as the
creation of the universe; return to the Unity.
Arabesque as the cosmic spiral, the journey towards the Unity
through multiplicity, Chahar-Bagh madrassa, Isfahan, 1706-14
A.D.
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* For a Hemispherical Dome under Self
Weight:
cos1
coscos1 2
prN
If then: 0N
0coscos1 2
Then
1
2
51cos
Or
0551
The Meridional Force at this Angle Is
Inversely Proportional to the Golden Ratio:
)1
(cos1
1
prprN
Golden Angle
Golden Force
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نصف که) ماکزیمم فشاری تنش و پوسته سطح واحد وزن :با برابرند ترتیب به (است النهاری
:ب
= (300) X 13 / 0.20
= 19500 kg/m2 = 1.95 kg/cm2
< fc = 30 kg/cm2 O.K.
مخرج و صورت از گنبد ضخامت باال، معادله در که شود توجه .است ضخامت از مستقل شده محاسبه تنش و گردد می حذف
p = rt = 1500 X 0.2 = 300 kg/m2
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وزن بار تحت الملک تاج گنبد در النهاری نصف های تنش (مربع متر بر نیوتن 500000 = فشاری مقاومت)
:با است برابر (است مداری که) ماکزیمم کششی تنش
= 300 X 13 / 0.20
= 19500 kg/m2 = 1.95 kg/cm2
< ft = 3 kg/cm2 O.K.
مخرج و صورت از گنبد ضخامت باال، معادله در که شود توجه .است ضخامت از مستقل شده محاسبه تنش و گردد می حذف
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وزن بار تحت الملک تاج گنبد در مداری های تنش (مربع متر بر نیوتن 50000 = کششی مقاومت )
:بزرگ قطر با حتی ،وزن بار تحت بنایی گنبدهای برای
فشاری مقاومت از تر کوچک بسیار ماکزیمم فشاری تنش -1 .است
معموال است مداری صورت به که ماکزیمم کششی تنش -2 .است کششی مقاومت از تر کوچک
.کند می قائم های ترک ایجاد صورت این غیر در - رینگ از توان می قائم های ترک ایجاد از جلوگیری برای •
.کرد استفاده بند پشت دیوار یا کش، یا کششی، های از قبل توان می قائم های ترک ایجاد از جلوگیری برای •
تغییر را قوس شعاع زاویه به رسیدن .داد
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Majid-i-Jami, Ushturjan, 1315-16 A.D.
Majid-i-Jami, Ushturjan, 1315-16 A.D.
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Rahim Khan Mosque, Isfahan, 19th Century A.D.
Rahim Khan Mosque, Isfahan, 19th Century A.D.
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Rahim Khan Mosque, Isfahan, 19th Century A.D.
Rahim Khan Mosque, Isfahan, 19th Century A.D.
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Masjid-i-Naw, Isfahan, 1854 A.D.
Masjid-i-Naw, Isfahan, 1854 A.D.
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Masjid-i-Naw, Isfahan, 1854 A.D.
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End
Membrane Stresses in Shells