Introduction to Structural Analysis - UMDaustin/ence353.d/lecture...Introduction Connecting...
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Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assum Introduction to Structural Analysis Mark A. Austin University of Maryland [email protected] ENCE 353, Fall Semester 2020 September 3, 2020
Transcript of Introduction to Structural Analysis - UMDaustin/ence353.d/lecture...Introduction Connecting...
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Introduction to Structural Analysis
Mark A. Austin
University of Maryland
ENCE 353, Fall Semester 2020
September 3, 2020
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Overview
1 IntroductionCourse Introduction
2 Connecting Mechanics to Analysis
3 Connecting Analysis to Structural DesignConnecting Analysis to Structural Design
4 Theory of StructuresStatically Determinate and Indeterminate Structures
5 Simplifying AssumptionsSmall Displacements, Linear Systems Behavior
6 Symmetries
Part 2
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Introduction
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Definition of Structural Mechanics
Mechanics. Branch of science that deals with response of matterto forces.
Civil Engineering:
Structural mechanics (� - ✏):material displacement.
Geomechanics (� - ✏): pressure,temperature, displacements.
Fluid mechanics (� - ✏): pressure,velocities.
Other domains:
Biomechanics (� - ✏): eye, heart,biological systems that grow!
�
✏
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
ConnectingMechanics to Analysis
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Pathway from Mechanics to System-Level Behavior
From material-level mechanics to building-system response:
�(x) =hM(x)EI
i
Material
Response
Section
Response
Beam
Response
Building System
Response
integrateintegrate assemble
✏(x , y)
Strain
�(x , y)
Stress Curvature
dy/dx
Slope
y(x)
Deflection
How will the integration work?
Analytical Procedures: The math needs to be ”nice” ...
Numerical Proedures: Compute approximate solutions !linear algebra, numerical algorithms, structural analysis andfinite elements.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
ConnectingAnalysis to Design
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Framework for Analysis and Design
Creating an Analysis Model
Abstract from considerationdetails not needed fordecision making.
Validate that modelcaptures essential aspects ofreal-world behavior.
Decision making needed fordesign.
Perfect is the enemy ofgood. Mathematical modeland decision making doesnot need to be perfect inorder to be useful.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Connecting Analysis to Design
Structural Design. Sequence of analyses punctuated by decisionmaking.
Determine types and magnitudes of loads and forces acting onthe structure.
Determine context of project: geometric constraints,architectural constraints, geological conditions, urbanregulations, cost, schedule, etc.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Connecting Analysis to Design
Generate structural system alternatives.
Analyze one or more of the alternatives.
Select and perform detailed design.
Implement/build.
Analysis and decision makingprocedures complicated byuncertainties in loading, materialproperties, etc. State-of-the-artmethods compensate foruncertainties with safety factors.
New structural systems may also require an experimental testingphase to verify behavior and achievable system performance.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Connecting Analysis to Design
Real-World and Idealized Abstractions
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Connecting Analysis to Design
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Connecting Analysis to Design
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Theory of Structures
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Statically Determinate Structures
Definition. Can use statics to determine reactions and distributionof element-level forces. Determinacy is not a↵ected by details ofloading.
Two-Dimensional Problems
XFx
= 0,X
Fy
= 0,X
Mz
= 0. (1)
Three-Dimensional Problems
XFx
= 0,X
Fy
= 0,X
Fz
= 0. (2)
XM
x
= 0,X
My
= 0,X
Mz
= 0. (3)
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Statically Determinate Structures
Example 1. Simply supported beam:
A B
VB
VA
HA
PP
Three equations of equilibrium:P
Fx
= 0,P
Fy
= 0,P
Fz
= 0.
Three unknowns: VA
, HA
and VB
! Can use statics to solve.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Statically Determinate Structures
Example 2. Small truss structure:
A B
VB
VA
HA
P P
PP
P
Use statics to find support reactions VA
, HA
and VB
.
Compute member forces by considering equilibrium ofindividual joints.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Statically Indeterminate Structures
Definition. Statics alone are not enough to find reactions. Needto find additional information (e.g., material behavior).
Example 1. Simply supported beam:
VA
HA
VB
A B
HB
P P
Three equations of equilibrium:P
Fx
= 0,P
Fy
= 0,P
Fz
= 0.
Four unknowns: VA
, HA
, VB
and HB
! 4 > 3 ! staticallyindeterminate to degree 1.
Introduction Connecting Mechanics to Analysis Connecting Analysis to Structural Design Theory of Structures Simplifying Assumptions Symmetries
Statically Indeterminate Structures
Example 2.
VB
A B
VA
HA
VC
PP
Three equations of equilibrium. Four unknowns: VA
, HA
, VB
andVC
! 4 > 3 ! statically indeterminate to degree 1.
Example 3. Multi-material Truss Element.
Material behavior definedby � � ✏ characteristics.Need to maintaingeometric compatibility.
Material A Material B
P P
