HW #12 Notes
Moment Distribution Method
Frames
Chapter 12 Displacement Method of Analysis: Moment Distribution (pg 487)
Fixed End Moments (FEM) are the moments at the walls or fixed joints of a loaded member
Determined from the given table depending on th
Overview
I Tributary Area
1) Beams and girders on different level
2) Beams and girders at the same level
II Influence Area and LL reduction factor
III Example problem
I. Tributary Area
1) Beams and girders on different level
I. Tributary Area
1.25
1.25
Fi
PROBLEM 1
P := 20
L := 8
reactions
RA :=
RC :=
P L
2L
P L
2L
= 10
= 10
moment at B
M B := RA L = 80
slope at A and
C
tCA
A =
L
tCA :=
1 1
5120
M B 2 L L =
2 EI
EI
tCA
320
A :=
=
2 L
EI
C = A + AC
1 1
640
AC := M B 2 L =
2 EI
EI
320
C := A + AC =
EI
defle
CIVIL 3610 Structural Analysis
Krzysztof G. Waszczuk
Structural Loads
Dead Load
Live Load
Environmental Loads
Other loads and load effects
Structural Loads
Dead Load
Weight of structural and non-structural components
Live Load
Weight of people
We
CIVIL 3610 Structural Analysis
Krzysztof G. Waszczuk
Syllabus
Krzysztof G. Waszczuk
306C Ramsay Hall
waszczuk@auburn.edu
Office Hours: Wednesday and Friday 2:00pm
3:00pm or by appointment
Syllabus
Class Schedule
Lectures: Monday, Wednesday and Friday at
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HW #11 Notes
Slope-Deflection Equations(includes force method)
Chapter 11 Displacement Method of Analysis: Slope-Deflection Equations (pg 451)
Slope-Deflection Equations
4 EI
2 EI
M AB=
A=
L
L B
4 EI
2 EI
M BA =
B =
L
L A
Fixed-End Moments (FEM)
For Int
HW #10 NotesForce Method for Analyzing Indeterminate Structures(with virtual work)
Chapter 10 Analysis of Statically Indeterminate Structures by the Force Method (pg 395)
Method
Unknowns
Equations Used for Solution
Coefficients of the
Unknowns
Force Metho
HW #9 NotesVirtual Work Method for Flexural DeformationsBeams & Frames
Chapter 9 Deflections Using Energy Methods, Section 7 Method of Virtual Work Beams & Frames (pg 364)
Virtual Work Equations for Beams and Frames
To find an external displacement of a
Exam 1
Review
Determinacy and Stability
Statically Determinate: r = 3n
Statically Indeterminate: 3 > 3n
Unstable r < 3n
o If 3 3n it is unstable if member reactions are concurrent,
parallel, or some of the components form a collapsible mechanism
(flopp
EXAM #2
Chapter 3
ANALYSIS OF STATICALLY DETERMINATE TRUSSES
Determinacy and Stability of Beams and Frames
Statically Determinate
Statically Indeterminate
Unstable
r=3 n
r >3 n
r <3 n
OR
r 3 n
Determinacy and Stability of Trusses
Number of Bars or Memb
Virtual Work Method for Statically Determinate Trusses
Determinacy
1. Check the truss for determinacy and stability to ensure the truss is statically determinate using the
bar forces (b), support reactions (r), truss joints (j), & the following equations
FINAL EXAM InformationSTRUCTURAL ANALYSIS
12/7(Mon) @ 12:00
Exams & Material
Exam #1
o Chapter 2
Determinacy and Stability
Reactions
o Chapter 4
Internal Forces in Beams and Frames
At a Point
Functions
Diagrams (Beams and Frames)
Superposition
Ex
Chapter 10
ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE FORCE METHOD
#1 STATICALLY INDETERMINATE STRUCTURES
Method
Unknowns
Equations Used for Solution
Force Method
Forces
Displacement Method
Displacements
Compatibility and force
displacement
Eq
Chapter 11Displacement Method of Analysis: SLOPE-DEFLECTION EQUATIONS
(page 451)
#1 Displacement Method of Analysis: General Procedures
4 EI
M AB=
Angular Displacement at A, A :
L A
4 EI
M BA =
Angular Displacement at B, B :
L B
6 EI
M AB=M BA =M =
L2
Chapter 8
DEFLECTIONS
#1 DEFLECTION DIAGRAMS AND THE ELASTIC CURVE
Deflections at specified points must be determined if one is to analyze a statically
indeterminate structure
Deflections that have a Linear Elastic Material Response- a structure subjecte
Chapter 2: BOOK PROBLEMS &
EXAMPLES
PROBLEM: Example 2.9
GIVEN:
Beam with triangularly distributed loading
REQUIRED: Determine the reactions on the beam.
SOLUTION:
F = bh= ( 155 )( 12 )=60 kN
@ 1/3(12) = 4m
F=lw= (5 )( 12 )=60 kN
@ (12) = 6m
F x = A x =0