Architectural Structures I: Lecture 16 - Strain and Material Behavior - Prof. A. Nichols, Study notes of Environmental Science

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Strain 1Lecture 16 Architectural Structures I ENDS 231 A RCHITECTURAL S TRUCTURES I: S TATICS AND S TRENGTH OF M ATERIALS ENDS 231D R. A NNE N ICHOLS S PRING 2008

sixteen elasticity& strain

lecture

Strain 2Lecture 16 Architectural Structures I ENDS 231

Deformations •

materials deform

axially loaded materials changelength - normal stress is load per unitarea -

STRAIN:

change in length over length - UNITLESS δ L ε =

Strain 4Lecture 16 Architectural Structures I ENDS 231

Shearing Strain •

deformationswith torsion

twist - change in angle of line - stress: - strain: - unitless (radians) τ^ γ

L

ρφ γ =

Strain 5Lecture 16 Architectural Structures I ENDS 231

Load and Deformation •

for stress, need P & A

for strain, need

& L

how? - TEST with load andmeasure - plot P/A vs. ε

Strain 7Lecture 16 Architectural Structures I ENDS 231

Behavior Types •

ductile - “necking”

true stress - engineering stress - (simplified) P^ A f = o P A f =

Strain 8Lecture 16 Architectural Structures I ENDS 231

Behavior Types •

brittle

semi-brittle

Strain 10Lecture 16 Architectural Structures I ENDS 231

Hooke’s Law •

straight line has constant slope

Hooke’s Law -

E

Modulus of elasticity - Young’s modulus - units just like stress f ε E 1 ε ⋅ = E f

Strain 11Lecture 16 Architectural Structures I ENDS 231

Stiffness •

ability to resist strain

steels - same E - differentyield points - differentultimate strength u f

Strain 13Lecture 16 Architectural Structures I ENDS 231

Elastic, Plastic, Fatigue •

elastic springs back

plastic has permanentdeformation - fatigue caused byreversed loadingcycles

Strain 14Lecture 16 Architectural Structures I ENDS 231

Plastic Behavior •

ductile at yield stress

Strain 16Lecture 16 Architectural Structures I ENDS 231

Poisson’s Ratio •

constant relationship betweenlongitudinal strain and lateral strain

sign! z x y x

strain

axial

strain

lateral

ε ε ε ε μ

E

f

x z y μ ε ε

μ

Strain 17Lecture 16 Architectural Structures I ENDS 231

Calculating Strain •

from Hooke’s law

substitute - get

ε ⋅ = E f L E P A δ ⋅ = PL AE = δ

Strain 19Lecture 16 Architectural Structures I ENDS 231

why we use f ave - increase in stress atchanges in geometry - sharp notches - holes - corners -

Stress Concentrations

Strain 20Lecture 16 Architectural Structures I ENDS 231 S2008abn 2 2 max max f P A f o v = = −

if we need to knowwhere max f and f v happen:

Maximum Stresses

F o P A f = max 1 cos 0 = → ° = θ θ 5 . 0 sin cos 45 = = → ° = θ θ θ