ENCE$353:$An$Overview$of$Structural$...
Transcript of ENCE$353:$An$Overview$of$Structural$...
![Page 1: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/1.jpg)
ENCE 353: An Overview of Structural Analysis and Design
Mark Aus?n Fall Semester 2011
![Page 2: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/2.jpg)
Outline • Objec?ve of Structural Engineering • Structural Engineering Process • Types of loads • Types of structures • Civil Engineering Materials
• Load paths in structures • How can structures fail? • Summary
![Page 3: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/3.jpg)
Objec?ves of Structural Engineering
Structural engineering is the … ….science and art of designing and making, with economy and
elegance, buildings, bridges, frameworks, and other structures so that they can safely resist the forces to which they may be subjected.
Design: process of determining loca?on, material, and size of structural elements to resist forces ac?ng in a structure
![Page 4: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/4.jpg)
Structural Design Process
• Determine types magnitudes of loads and forces ac?ng on the structure
• Determine structural context – geometric and geological informa?on – cost / schedule / height/ etc. limita?ons
• Generate alterna?ve structural systems (e.g., moment resistant frame, materials selec?on),
• Analyze one or more alterna?ves • Select and perform detailed design • Implement (usually done by contractor)
Note: New structural systems may also require an experimental testing phase to verify behavior and system performance.
![Page 5: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/5.jpg)
Formal Approach to Structural Design
![Page 6: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/6.jpg)
Formal Approach to Structural Design
![Page 7: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/7.jpg)
Types of loads • Dead loads • Live loads • Dynamic loads (e.g., trains, equipment)
• Wind loads
• Earthquake loads • Thermal loads
• SeZlement loads
![Page 8: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/8.jpg)
Dead Loads • weight of the structure itself
– floors, beams, roofs, decks, beams/stringers, superstructure
• loads that are “always there”
![Page 9: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/9.jpg)
Live Loads
• People, furniture, equipment • Loads that may move or change mass or weight
• Minimum design loadings are usually specified in the building code
![Page 10: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/10.jpg)
Load Example: Live Load in Ballroom
Live Load = 100 lb/ft^2 Ballroom
![Page 11: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/11.jpg)
Dynamic Loads • Moving loads (e.g., traffic) • Impact loads
• Gusts of wind • Loads due to cycling machinery
![Page 12: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/12.jpg)
Load Example: Dynamic Load
HVAC
F
t
![Page 13: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/13.jpg)
Load Example: Water in a dam
Water, ρ = density
h p = ρgh
![Page 14: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/14.jpg)
Earthquake Loads • Structure loaded when base is shaken • Response of structure is dependent on the frequency of mo?on
• When frequencies match with natural frequency of structure -‐ resonance
![Page 15: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/15.jpg)
Load Example: Earthquake Load
Base Motion
Earthquake Load
Earthquake Load
![Page 16: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/16.jpg)
![Page 17: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/17.jpg)
SeZlement
![Page 18: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/18.jpg)
Forces Ac?ng in Structures
• Forces induced by gravity – Dead Loads (permanent): self-‐weight of structure and aZachments
– Live Loads (transient): moving loads (e.g. occupants, vehicles)
• Forces induced by wind • Forces induced by earthquakes • Forces induced by rain/snow • Fluid pressure
![Page 19: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/19.jpg)
Forces Ac?ng in Structures
Vertical: Gravity Lateral: Wind, Earthquake
![Page 20: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/20.jpg)
Global Stability
Sliding Overturning
![Page 21: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/21.jpg)
Forces in Structural Elements
University of Massachusetts Amherst
100 lb
Compression
100 lb
Tension
![Page 22: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/22.jpg)
Forces in Structural Elements (cont.)
100 lb
Bending
Torsion
![Page 23: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/23.jpg)
Some Types of Structures • Arch • Planar Truss • Beam/Girder
• Flat plate • Braced and Rigid Frames
• Folded Plate and Shell Structures • Cable Suspended Structure
![Page 24: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/24.jpg)
Arch
Arch
Design objective: Structure needs to work and be aesthetically pleasing!! Analysis objective: What shape should the arch be so that forces can be transferred to the foundation through compression mechanisms alone?
![Page 25: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/25.jpg)
![Page 26: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/26.jpg)
Planar Truss
![Page 27: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/27.jpg)
Planar Truss
Truss C
T
C C T
Forces in Truss Members
![Page 28: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/28.jpg)
![Page 29: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/29.jpg)
Truss
• Combina?on of square and triangle – Both ver?cal and lateral support
![Page 30: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/30.jpg)
Beam/Girder
![Page 31: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/31.jpg)
![Page 32: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/32.jpg)
Frames
Braced Rigid
![Page 33: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/33.jpg)
Frames Con?nued
Frame
Analysis objective: We want to compute the distribution of forces – axial, bending moment, shear forces – throughout the structure. What are the displacements? Will the frame structure be stable?
![Page 34: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/34.jpg)
![Page 35: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/35.jpg)
Flat Plate
![Page 36: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/36.jpg)
Folded Plate
![Page 37: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/37.jpg)
Shells
Circular Shell Structure Lattice Shell Structure
![Page 38: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/38.jpg)
Cable Suspended Structure
Analysis objective: What are the forces in the cable structure? How will the cable profile shape change with different distributions of live load? What are the bending moments in the bridge deck?
![Page 39: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/39.jpg)
![Page 40: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/40.jpg)
Cable Stayed Bridge
![Page 41: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/41.jpg)
![Page 42: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/42.jpg)
Load Paths in Structures
• Load Path is the term used to describe the path by which loads are transmiZed to the founda?ons
• Different structures have different load paths • Some structures have only one path
• Some have several (redundancy good)
![Page 43: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/43.jpg)
Load Path in Framed Structure
![Page 44: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/44.jpg)
Structural Components
• Beams • Girders • Columns
• Floors • Founda?ons
Column Girder
Beam
![Page 45: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/45.jpg)
Load Path
• Floor
• Beams
• Girders
• Columns
• Founda?on
• Soil/Bedrock
![Page 46: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/46.jpg)
Flooring
• Composed of a subfloor and floor covering – Usually leave space for ductwork, wiring, etc. – Floor covering ranges from applica?on to applica?on
![Page 47: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/47.jpg)
Beams
• AZached between the girders – Take load from the flooring system
– Transfer it to the girders
– Generally solid squares, I-‐beams
![Page 48: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/48.jpg)
Girders
• AZached column-‐to-‐column – Take the load from the beams
– Transfer it to the columns
– Generally shaped as an I-‐Beam
![Page 49: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/49.jpg)
Founda?ons
• Support the building – Typically aZached to columns
• Types – Shallow
• Spread foo?ng – concrete strip/pad below the frost line • Slab-‐on-‐grade – concrete pad on the surface
– Deep • Drilled Shafs • Piles
![Page 50: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/50.jpg)
![Page 51: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/51.jpg)
Overview of Structural Behavior
Depends on:
• Material properties (e.g., steel, concrete). • Structural stiffness (e.g. axial stiffness, bending stiffness) • Structural strength (e.g., ultimate member strength).
Design challenges:
• If the structural stiffness is too low, then the displacements will be too large, • In dynamics applications a high structural stiffness may attract high inertia forces. • If the structural strength is too low, then the structural system may fail prematurely.
![Page 52: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/52.jpg)
Axial S?ffness
ΔL
T
T
Lo
Stiffness = T / ΔL
Example:
T = 100 lb ΔL = 0.12 in.
Stiffness = 100 lb / 0.12 in. = 833 lb/in.
![Page 53: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/53.jpg)
Bending S?ffness
Stiffness = Force / Displacement
Example:
Force = 1,000 lb Displacement = 0.5 in.
Stiffness = 1,000 lb / 0.5 in. = 2,000 lb/in.
Displacement
Force
![Page 54: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/54.jpg)
Defini?on of Stress
Section X
T
T
Section X
Stress = Force/Area
T
Example (English Units):
T = 1,000 lb (1 kip) A = 10 in2.
Stress = 1,000/10 = 100 lb/in2
Example (SI Units):
1 lb = 4.448 N (Newton) 1 in = 25.4 mm
T = 1,000 lb x 4.448 N/lb = 4448 N A = 10 in2 x (25.4 mm)2 = 6450 mm2
(1 in)2
Stress = 4448/6450 = 0.69 N/mm2 (MPa)
![Page 55: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/55.jpg)
Defini?on of Strain
ΔL
T
T
Lo
Strain = ΔL / Lo
Example:
Lo = 10 in. ΔL = 0.12 in.
Strain = 0.12 / 10 = 0.012 in./in.
Strain is dimensionless!! (same in English or SI units)
![Page 56: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/56.jpg)
Stress–Strain Behavior of Elas?c Mats.
Stress
Strain
E
E = Modulus of Elasticity = Stress / Strain
![Page 57: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/57.jpg)
Types of Stress-‐Strain Behavior Stress
Strain
E
(a) Linear Elastic
Stress
Strain (b) Non-linear Elastic
Stress
Strain (c) Elastic-plastic
Stress
Strain (d) Non-linear Plastic
Plastic strain Plastic strain
![Page 58: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/58.jpg)
Types of Structural Elements – Beams
Tension
Compression
Loads
![Page 59: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/59.jpg)
Engineering Proper?es of Structural Elements
• Strength – Ability to withstand a given stress without failure
• Depends on type of material and type of force (tension or compression)
Tensile Failure Compressive Failure
![Page 60: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/60.jpg)
Engineering Proper?es of Materials • Steel
– Maximum stress: 40,000 – 120,000 lb/in2
– Maximum strain: 0.2 – 0.4 – Modulus of elas?city: 29,000,000 lb/in2
• Concrete – Maximum stress: 4,000 – 12,000 lb/in2
– Maximum strain: 0.004 – Modulus of elas?city: 3,600,000 – 6,200,000 lb/in2
• Wood Values depend on wood grade. Below are some samples – Tension stress: 1300 lb/in2 – Compression stress: 1500 lb/in2 – Modulus of elas?city: 1,600,000 lb/in2
![Page 61: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/61.jpg)
Types of Structural Elements – Bars and Cables
Bars can carry either tension or compression Cables can only carry tension
![Page 62: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/62.jpg)
S?ffness of Different Structural Shapes
Stiffest
Stiffer Stiff
![Page 63: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/63.jpg)
Providing Stability for Lateral Loads
Racking Failure of Pinned Frame
Braced Frame Infilled Frame Rigid Joints
![Page 64: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/64.jpg)
Failure Mechanisms
Structural failure refers to loss in the load-carrying capacity of a component or member within a structure.
Failure is initiated when the material is stressed to the strength limit, thus causing fracture or excessive deformations.
Ultimate failure is usually associated with extreme events. The structural engineer needs to prevent loss of life by prohibiting total collapse of the structural system.
![Page 65: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/65.jpg)
Failure due to Dynamic Instability Failure to understand aeroelastic flutter can be catastrophic.
Failure of the Tacoma Narrows bridge completely changed the way in which suspension bridges are analyzed and designed.
![Page 66: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/66.jpg)
Failure due to neglect …
Collapsed I35 W. Mississippi Bridge, August 1, 2007.
Key problems: lack of funding; poor maintenance.
![Page 67: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/67.jpg)
Frame buildings can have also be built with concrete columns and beams (as opposed to steel)
1971 San Fernando earthquake showed that many concrete frames were briZle
Poten?al for collapse at drifs of about 0.01 (lower than for steel buildings)
There are thousands of these buildings in California and occupants have not been no?fied
Olive View Hospital M 6.7 1971 San Fernando Earthquake
Failure due to lack of Ductility in Concrete Columns
![Page 68: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/68.jpg)
Northridge 118 FWY
Example of failure of a briZle concrete column (pre-‐1975 code)
![Page 69: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/69.jpg)
Example of “duc?le” behavior of concrete columns. Although the parking structure performed poorly, the exterior columns did not fail.
![Page 70: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/70.jpg)
Mexico City Earthquake, 1996
![Page 71: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/71.jpg)
Failure due to liquefaction
![Page 72: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/72.jpg)
Sometimes you are simply in the wrong place at the wrong time ...
Christchurch, New Zealand, 2011.
![Page 73: ENCE$353:$An$Overview$of$Structural$ Analysis$and$Design$austin/ence353.d/lecture-material2011/ENCE... · •Structural stiffness (e.g. axial stiffness, bending stiffness) •Structural](https://reader033.fdocuments.us/reader033/viewer/2022041413/5e19953d3df7010ac76d5aca/html5/thumbnails/73.jpg)
Summary • Structural Engineering:
– Iden?fies loads to be resisted – Iden?fies alterna?ves for providing load paths (arch, truss, frame, ...)
– Designs structure to provide safe and economical load paths (material, size, connec?ons)
– To be economical and safe, we must be able to predict what forces are in structure.
Acknowledgement: University of Massachusetts Amherst .