The document discusses the plastic analysis of slabs using the kinematic method. It begins by introducing slabs and their structural modeling. It then covers yield lines and the assumption that they can be approximated as bisectors. Several examples are presented of determining the plastic moment capacity of different types of slabs, including squared, hexagonal, and circular slabs with various support conditions, through satisfying the principle of virtual work by equating external and internal work. The method is demonstrated on more complex slab layouts as well.
This poster was created in LaTeX on a Dell Inspiron laptop with a Linux Fedora Core 4 operating system. The background image and the animation snapshots are dxf meshes of elastic waveform solutions, rendered on a Windows machine using 3D Studio Max.
This is a Question Papers of Mumbai University for B.Sc.IT Student of Semester - II [Computer Graphics] (Old Course). [Year - September / 2013] . . .Solution Set of this Paper is Coming soon..
This poster was created in LaTeX on a Dell Inspiron laptop with a Linux Fedora Core 4 operating system. The background image and the animation snapshots are dxf meshes of elastic waveform solutions, rendered on a Windows machine using 3D Studio Max.
This is a Question Papers of Mumbai University for B.Sc.IT Student of Semester - II [Computer Graphics] (Old Course). [Year - September / 2013] . . .Solution Set of this Paper is Coming soon..
Simulation and Experimental Studies on Composite BeamsIJERA Editor
A composite beam a one dimensional structure or a rod all of them are sectional dimensions in which width and height are much smaller in comparison to the structure. In structural applications longer beams are more frequently used. In this work a composite beam is manufactured with glass and epoxy combination. And stress analysis is carried out using derived analytical expressions. This research work carried out will enable to determine the beam strength due to bending loads. The importance of fiber reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. Mat lab codes are generated to implement analytical equations of the composite beam. The analytical results are validated by performing experiments on composite beams. In this investigation, two different composite beams have been tested and compared the experimental results with the analytical results.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
__ae2_22_PLASTIC ANALYSIS OF SLABS_YIELD LINES.pptx
1. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
PLASTIC ANALYSIS OF SLABS
SLAB: Structural element contained in a plane (the third
dimension is much smaller than the other two).
The load direction is perpendicular to the structure plane
3. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
1.- ELASTIC ANALYSIS OF GRIDS
1.1.- COMPATIBILITY METHOD
1.2- SLOPE DEFLECTION METHOD
2.- PLASTIC ANALYSIS OF STRUCTURES
2.1- PLASTIC ANALYSIS OF BEAMS
2.2- PLASTIC ANALYSIS OF FRAMES
2.2.1- KINEMATIC METHOD
2.2.2- INCREMENTAL ANALYSIS. HINGE BY HINGE METHOD
3.- INTRODUCTION TO SECOND ORDER ANALYSIS OF STRUCTURES
2.3- PLASTIC ANALYSIS OF SLABS.
FEBRUARY
MARCH
APRIL
4. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
YIELD LINES: líneas de rotura (plástica)
YIELD LINES = ROTATION LINE
YIELD LINES METHOD
5. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
ASSUMPTION: YIELD LINES = BISECTRICES
STUCTURAL MODEL OF A SLAB (PLAN)
MODELO ESTRUCTURAL DE LOSA (PLANTA)
6. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
YIELD LINES: BISECTRICES
YIELD LINES CAN BE POSSITIVE OR NEGATIVE
STUCTURAL MODEL OF A SLAB (PLAN)
MODELO ESTRUCTURAL DE LOSA (PLANTA)
7. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
VERY IMPORTANT: DRAW THE CROSS SECTION!!!!
Based in the VIRTUAL WORK PRINCIPLE: Wext = Wint
CROSS
SECTION
CROSS
SECTION
PLAN
PLAN
8. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
Wext = P1 x v/2 + P2 x v/2 = P1 x v = q L2 /2 x g1 x L/2
CROSS
SECTION
CROSS
SECTION
PLAN
PLAN
Wint= Mp x L x (g1 + g2) = 2 L Mp x g1
P1 = P2 = L/2 x L x q = q L2 /2
q L2 x g1 x L/4 = 2 L Mp x g1 Mp = q L2 /8
Wint= Wext
9. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
Wext = P1 x v/2 + P2 x v/2 = P1 x v = q L2 /2 x g1 x L/2
CROSS
SECTION
CROSS
SECTION
PLAN
PLAN
Wint= L x Mp x (g1 + g2) = 2 L Mp x g1
P1 = P2 = L/2 x L x q = q L2 /2
q L2 x g1 x L/4 = 2 L Mp x g1 Mp = q L2 /8
Wint= Wext
Wext = P1 x v/2 + P2 x v/2 = P1 x v = q L2 /2 x g1 x L/2
Wint= L x Mp + L x Mp x (g1 + g2) + L x Mp = 4L Mp x g1
P1 = P2 = L/2 x L x q = q L2 /2
q L2 x g1 x L/4 = 4 L Mp x g1 Mp = q L2 /16
10. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
YIELD LINES: BISECTRICES
YIELD LINES CAN BE POSSITIVE OR NEGATIVE
1.- Yield lines divide the slab into rigid regions which remain plane through the
collapse;
2.- Yield lines are straight;
3.- Axes of rotation generally lie along line of supports and pass over columns;
4.- Yield lines between adjacent rigid regions must pass through the intersection point
of the axes of rotation of those regions;
5.- Yield lines must end at a slab boundary;
6.- Continuous supports repel and a simple support attract yield lines.
11. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
EXTERNAL WORK
SQUARED SLAB
PINNED SUPPORTED
ALONG FOUR SIDES
REMEMBER:
TO MEASURE THE
EXTERNAL WORK,
REGIONS CROSS
SECTIONS MUST BE
PERPENDICULAR TO
ROTATION LINES
(rotation lines are
usually the sides of the
slab)
12. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
SQUARED SLAB
PINNED SUPPORTED
ALONG FOUR SIDES
INTERNAL WORK
REMEMBER: TO
MEASUSER INTERNAL
WORK, CROSS
SECTIONS MUST BE
PERPENDICULAR TO
YIELD LINES SO WE CAN
CONSIDER ITS TRUE
DIMENSION
13. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
SQUARED SLAB
PINNED SUPPORTED
ALONG FOUR SIDES
INTERNAL WORK
REMEMBER: TO
MEASUSER INTERNAL
WORK, CROSS
SECTIONS MUST BE
PERPENDICULAR TO
YIELD LINES SO WE CAN
CONSIDER ITS TRUE
DIMENSION
14. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
SQUARED SLAB
PINNED SUPPORTED
ALONG FOUR SIDES
¿INTERNAL WORK?
TO MEASUSER
INTERNAL WORK, AND
USE THE ROTATION OF
THE REGION SIDE
INSTEAD OF THE
ROTATION OF THE
YIELD LINE, WE CAN
USE THE YIELD LINES
PROJECTIONS LENGTH
15. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
SQUARED SLAB
PINNED SUPPORTED
ALONG FOUR SIDES
INTERNAL WORK
TO MEASUSER
INTERNAL WORK, AND
USE THE ROTATION OF
THE REGION SIDE
INSTEAD OF THE
ROTATION OF THE
YIELD LINE, WE CAN
USE THE YIELD LINES
PROJECTIONS LENGTH
20. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
VIRTUAL WORK PRINCIPLE: EXTERNAL WORK = INTERNAL WORK
Wext = 6 x q x L x a /2 x v/3 = q L a x g1
Wint = 6 Lx Mp x g1
q L a x g1 = 6 Lx Mp x g1 Mp = q a /6
Wext = 6 x q x L x a /2 x v/3 = q L a x g1
Wint = (6 Lx Mp x g1) x 2
q L a x g1 = 12 Lx Mp x g1 Mp = q a /12
22. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
VIRTUAL WORK PRINCIPLE: EXTERNAL WORK = INTERNAL WORK
Wext = pi R2 x q x v/3 = pi R2 x q x R g1 /3
Wint = 2 pi R x Mp x g1
pi R2 x q x R g1 /3 = 2 pi R x Mp x g1
Mp = q a /6
Wext = pi R2 x q x v/3 = pi R2 x q x R g1 /3
Wint = 2 x (2 pi R x Mp x g1)
pi R2 x q x R g1 /3 = 4 pi R x Mp x g1
Mp = q a /12
24. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
BISECTRICES = YIELD LINE IS AN ASSUMPTION ACCURATE ENOUGH
Wext = 2 x(P1 x v/3 + P2 x v/2) + P5 x v/3 =
= 5 q x L2 v /12 = 5 q x L3 x g1/24
Wint = 3 L Mp x g1
Mp = 5 q x L2 /72
P1 = q x L2 /8
P2 = q x L2 /4
P5 = q x L2 /4
5 q x L3 x g1/24 = 3 L Mp x g1
29. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
A2 = 2 x 2 / 2 = 2 m2 its gravity center goes down 2v1/3
A3 = 2 x 5 = 10 m2 its gravity center goes down v1/2
v1 = 2 θ1 v2 = 2,5 θ1
Wext = 4 ( - A1 x v2 / 3 x q + A2 x 2 v1 x q + A3 x v2 x q) =
4 (-6,25 x 2,5 θ1 /3 x q + 2 x 2 x 2 θ1 /3 + 10 x 2 θ1 /2) = 4 (-5,208 + 2,67 + 10) q θ1 = 29,848 q θ1
Wint = 9 x 4 Mp θ1 = 36 Mp θ1
So when we equal external and internal work we get that: 36 Mp = 29,848 q Mp = 0,829 q
31. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
Wext = 4 (A1 x v2 / 3 x q - A2 x 2 v1 x q - A3 x v2 x q) = 4 (6,25 x 2,5 θ1 /3 x q - 2 x 2 x 2 θ1 /3 - 10 x 2 θ1 /2)
= 4 (5,208 - 2,67 - 10) q θ1 = - 29,848 q θ1
A NEGATIVE EXTERNAL WORK DOES NOT MAKE SENSE
THIS IS NOT THE TRUE COLLAPSE PATTERN
33. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
A1 = 5 x 2,5 / 2 = 6,25 m2 its gravity center goes up v1/3 v1 = 2,5 θ1
Wext = 4 (A1 x v1 / 3 x q) = 8,33 q 2,5 θ1 = 20,83 q
Wint = 4 x 5 x Mp x θ1+ 4 x 5 x Mp x θ1 = 40 Mp θ1
So when we equal external and internal work we get that: 40 Mp = 20,83 q Mp = 0,5207 q
35. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
A2 = 2 x 2 / 2 = 2 m2 its gravity center goes down 2v1/3
A3 = 2 x 5 = 10 m2 its gravity center goes down v1/2
v1 = 2 θ1
Wext = 4 (A2 x 2 v1 / 3 x q + A3 x v1 / 2 x q) = 4 ( 6,333 ) q 2 θ1 = 50,66 q
Wint = (2 x 8 + 4 x 5 ) Mp x θ1 = 36 Mp θ1
So when we equal external and internal work we get that: 36 Mp = 50,66 q Mp = 1,407 q
37. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
A4 = 9 x 2 = 18 m2 its gravity center goes up v1/2 v1 = 2 θ1
Wext = A1 x v1 / 2 x q = 9 q 2 θ1 = 18 q
Wint = 9 x Mp x θ1 = 9 Mp θ1
So when we equal external and internal work we get that: 9 Mp = 18 q Mp = 2 q
39. STRUCTURAL ANALYSIS II
PLASTIC ANALYSIS. KINEMATIC METHOD
A4 = 9 x 2 = 18 m2 its gravity center goes up v1/2 v1 = 2 θ1
Wext = A1 x v1 / 2 x q = 9 q 2 θ1 = 18 q
Wint = 9 x Mp x θ1 = 9 Mp θ1
So when we equal external and internal work we get that: 9 Mp = 18 q Mp = 2 q
THE HIGHEST Mp (or lowest qu)