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№1 слайд![Analysis of Statically](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img0.jpg)
Содержание слайда: Analysis of Statically Determinate Structures
ECE479 Structural Analysis II
Text Book
Structural Analysis
by
R. C. Hibbeler
№2 слайд![Lecture Outlines Idealized](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img1.jpg)
Содержание слайда: Lecture Outlines
Idealized Structure
Equations of Equilibrium
Determinacy and Stability
№3 слайд![Intended Learning Outcomes By](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img2.jpg)
Содержание слайда: Intended Learning Outcomes
By the end of today’s session student’s should be able to:
Idealize a structure
Determine Determinacy and Stability of structure
№4 слайд![Why Idealize Structure? Exact](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img3.jpg)
Содержание слайда: Why Idealize Structure?
Exact analysis --- Not possible
Estimate
Loading and its point of application
Strength of the Materials
№5 слайд![Support Connections Types ---](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img4.jpg)
Содержание слайда: Support Connections
Types --- Usually Three
Pin supported connection
Roller supported connection
Fixed supported connection
№6 слайд![Support Connections- Roller](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img5.jpg)
Содержание слайда: Support Connections- Roller support
Roller support - Deck of concrete bridge (One section considered roller supported on other section)
№7 слайд![Support Connections- Roller](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img6.jpg)
Содержание слайда: Support Connections- Roller support
Roller support - Used to supports prestressed girders of a highway bridge.
№8 слайд![Roller supported Concrete](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img7.jpg)
Содержание слайда: Roller supported Concrete connection
№9 слайд![Support Connections Pin](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img8.jpg)
Содержание слайда: Support Connections – Pin support
Pin support - Steel girder Railway bridge
№10 слайд![Support Connections Fixed](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img9.jpg)
Содержание слайда: Support Connections – Fixed support
№11 слайд![](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img10.jpg)
№12 слайд![Equations of Equilibrium For](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img11.jpg)
Содержание слайда: Equations of Equilibrium
For complete static equilibrium in 2D, three requirements must be met:
1. External Horizontal forces balance (translation).
2. External Vertical forces balance (translation).
3. External Moments balance about any point (rotational).
№13 слайд![Equations of Equilibrium For](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img12.jpg)
Содержание слайда: Equations of Equilibrium
For two-dimensional system of forces and moments, the equilibrium equations are:
1. Fx = 0
2. Fy = 0
3. z = 0
№14 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img13.jpg)
Содержание слайда: Determinate vs Indeterminate Structure
When all the forces in a structure can be determined from the equilibrium equations, the structure is referred to as statically determinate.
When the unknown forces in a structure are more than the available equilibrium equations, that structure is known as statically indeterminate.
№15 слайд![Determinacy For a coplanar](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img14.jpg)
Содержание слайда: Determinacy
For a coplanar structure, there are at most three equilibrium equations for each part.
If there is a total of n parts and r force and moment reaction components, we have
r = 3n statically determinate
r > 3n statically indeterminate
№16 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img15.jpg)
Содержание слайда: Determinate vs Indeterminate Structure – Examples (Beams)
№17 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img16.jpg)
Содержание слайда: Determinate vs Indeterminate Structure – Examples (Beams)
№18 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img17.jpg)
Содержание слайда: Determinate vs Indeterminate – Examples (Pin-connected structures)
№19 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img18.jpg)
Содержание слайда: Determinate vs Indeterminate – Examples (Pin-connected structures)
№20 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img19.jpg)
Содержание слайда: Determinate vs Indeterminate Structure – Examples (Frame)
№21 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img20.jpg)
Содержание слайда: Determinate vs Indeterminate Structure – Examples (Frame)
№22 слайд![Determinate vs Indeterminate](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img21.jpg)
Содержание слайда: Determinate vs Indeterminate Structure – Examples (Frame)
№23 слайд![Stability What conditions are](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img22.jpg)
Содержание слайда: Stability
What conditions are necessary To ensure equilibrium of a structure?
A structure will be unstable if
there are fewer reactive forces than equations of equilibrium (Partial Constraints)
or
there are enough reactions and instability will occur if the lines of action of reactive forces intersect at a common point or are parallel to one another (Improper Constraints)
№24 слайд![Stability Example Partial](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img23.jpg)
Содержание слайда: Stability – Example – Partial Constraints
№25 слайд![Stability Example Improper](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img24.jpg)
Содержание слайда: Stability – Example – Improper Constraints
№26 слайд![Stability Example Improper](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img25.jpg)
Содержание слайда: Stability – Example – Improper Constraints
№27 слайд![Stability r lt nunstable r](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img26.jpg)
Содержание слайда: Stability
r < 3n unstable
r ≥ 3n unstable if member reactions are concurrent or parallel or some of the components form a collapsible mechanism
r --- Unknown reactions
n--- Members
Unstable structures Must be avoided in practice
№28 слайд![Stability Examples](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img27.jpg)
Содержание слайда: Stability – Examples
№29 слайд![Stability r lt nunstable r](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img28.jpg)
Содержание слайда: Stability
r < 3n unstable
r ≥ 3n unstable if member reactions are concurrent or parallel or some of the components form a collapsible mechanism
r --- Unknown reactions
n--- Members
№30 слайд![Summary Now You should be](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img29.jpg)
Содержание слайда: Summary
Now You should be able to:
Idealize a structure
Determine Determinacy and Stability of structure
№31 слайд![Assignment Issue Date - -](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img30.jpg)
Содержание слайда: Assignment 1
Issue Date 16-1-2017
Submission Date 23-1-2017
Classify each of the structures as statically determinate, statically indeterminate, or unstable. If indeterminate, specify the degree of indeterminacy
№32 слайд![Assignment Issue Date - -](/documents_6/7a0ed5c77c91a1e1a71d2aa81ff2ac0a/img31.jpg)
Содержание слайда: Assignment 1
Issue Date 23-1-2017
Submission Date 30-1-2017
Classify each of the structures as statically determinate, statically indeterminate, or unstable. If indeterminate, specify the degree of indeterminacy