four mechanics of materials Mechanics of Materials Mechanics of Materials Knowledge Required MECHANICS MATERIALS

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1 EEMENTS OF RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SRING 2014 Mechanics o Materials MECHNICS MTERIS lecture our mechanics o materials Mechanics o Materials 1 S2009abn Mechanics o Materials 7 Mechanics o Materials external loads and their eect on deormable bodies use it to answer question i structure meets requirements o stability and equilibrium strength and stiness other principle building requirements economy, unctionality and aesthetics Knowledge Required material properties member cross sections ability o a material to resist breaking structural elements that resist excessive delection deormation Mechanics o Materials 8 Mechanics o Materials 9 1

2 roblem Solving 1. STTICS: equilibrium o external orces, internal orces, stresses 2. GEOMETRY: cross section properties, deormations and conditions o geometric it, strains 3. MTERI ROERTIES: stress-strain relationship or each material obtained rom testing Stress stress is a term or the intensity o a orce, like a pressure internal or applied orce per unit area stress Mechanics o Materials 10 Mechanics o Materials 11 Design materials have a critical stress value where they could break or yield ultimate stress yield stress compressive stress atigue strength (creep & temperature) acceptance vs. ailure Design (cont) we d like actual F allowable stress distribution may vary: average uniorm distribution exists IF the member is loaded axially (concentric) Mechanics o Materials 12 Mechanics o Materials 13 2

3 Scale Eect model scale material weights by volume, small section areas structural scale much more material weight, bigger section areas scale or strength is not proportional: 3 2 Normal Stress normal stress is normal to the cross section stressed area is perpendicular to the load t or c Mechanics o Materials 9 S2009abn Mechanics o Materials 16 Shear Stress stress parallel to a surace Bearing Stress stress on a surace by contact in compression v ave td p td Mechanics o Materials 17 Mechanics o Materials 18 3

4 Bending Stress normal stress caused by bending Torsional Stress shear stress caused by twisting b Mc I M S v T J Mechanics o Materials 19 Mechanics o Materials 20 Structures and Shear what structural elements see shear? beams bolts splices slabs ootings walls wind seismic loads connections V Bolts connected members in tension cause shear stress connected members in compression cause bearing stress Mechanics o Materials 21 Mechanics o Materials 16 S2011abn 4

5 Single Shear seen when 2 members are connected Double Shear seen when 3 members are connected two areas F= Mechanics o Materials 17 v 2 d S2011abn 4 2 v 2 Mechanics o Materials d 4 S2011abn Bolt Bearing Stress compression & contact projected area F= Strain materials deorm axially loaded materials change length bending materials delect p projected td STRIN: change in length over length strain (S) Mechanics o Materials 19 S2011abn Mechanics o Materials 15 5

6 Shearing Strain deormations with shear parallelogram change in angles stress: strain: unitless (radians) s s tan Shearing Strain deormations with torsion twist change in angle o line stress: strain: unitless (radians) Stress & Strain 10 Stress & Strain 11 oad and Deormation or stress, need & or strain, need & how? TEST with load and measure plot / vs. Material Behavior every material has its own response 10,000 psi = 10 in Douglas ir vs. steel? Stress & Strain 12 Stress & Strain 13 S2005abn 6

7 Behavior Types ductile - necking true stress engineering stress (simpliied) o Behavior Types brittle semi-brittle Stress & Strain 14 Stress & Strain 15 Stress to Strain important to us in - diagrams: straight section INER-ESTIC recovers shape (no permanent deormation) Hooke s aw straight line has constant slope Hooke s aw E E Modulus o elasticity Young s modulus units just like stress E 1 Stress & Strain 16 Stress & Strain 17 7

8 Stiness ability to resist strain steels same E dierent yield points dierent ultimate strength u Isotropy & nisotropy ISOTROIC materials with E same at any direction o loading ex. steel NISOTROIC materials with dierent E at any direction o loading ex. wood is orthotropic Stress & Strain 18 Stress & Strain 19 Elastic, lastic, Fatigue elastic springs back plastic has permanent deormation atigue caused by reversed loading cycles lastic Behavior ductile at yield stress Stress & Strain 20 Stress & Strain 21 8

9 ateral Strain or what happens to the cross section with axial stress x E y z 0 strain in lateral direction negative x equal or isometric materials y z oisson s Ratio constant relationship between longitudinal strain and lateral strain lateral strain y axial strain x x y z E sign! z x Stress & Strain 15 S2006abn Stress & Strain 23 Calculating Strain rom Hooke s law substitute get () E E E Orthotropic Materials non-isometric directional values o E and ex: plywood laminates polymer composites Stress & Strain 24 Stress & Strain 25 9

10 Stress Concentrations why we use ave increase in stress at changes in geometry sharp notches holes corners Stress & Strain 26 Maximum Stresses i we need to know where max and v happen: 0 cos 1 Stress & Strain 27 max F 45 cos sin 0. 5 vmax 2 o o 2 max Maximum Stresses Deormation Relationships physical movement axially (same or zero) rotations rom axial changes 20 kn aluminum steel E relates to Stress & Strain 28 Torsion & Temp 18 ecture 16 10

11 Deormations rom Temperature atomic chemistry reacts to changes in energy solid materials can contract with decrease in temperature can expand with increase in temperature linear change can be measured per degree Thermal Deormation - the rate o strain per degree UNITS :, F length change: thermal strain: C no stress when movement allowed T T T T Torsion & Temp 19 ecture 16 Torsion & Temp 20 ecture 16 Coeicients o Thermal Expansion Wood Glass Steel Wrought Iron Copper Bronze Brass Material Concrete Cast Iron luminum Torsion & Temp 21 ecture 16 Coeicients () [in./in./f] 3.0 x x x x x x x x x x 10-6 Stresses and Thermal Strains i thermal movement is restrained stresses are induced 1. bar pushes on supports 2. support pushes back 3. reaction causes internal stress E Torsion & Temp 22 ecture 16 11

12 Superposition Method can remove a support to make it look determinant replace the support with a reaction enorce the geometry constraint Superposition Method total length change restrained to zero constraint: 0 p sub: E E T T 0 T T T E Torsion & Temp 23 ecture 16 Torsion & Temp 24 ecture 16 Dynamics kinematics time, velocity, acceleration linear motion s( t) v(0) t 1 at 2 angular rotation kinetics orces causing motion W = m g work conservation o energy 2 Dynamic Response Mechanics o Materials 43 S2007abn Mechanics o Materials 44 S2007abn 12

13 Dynamic Response period o vibration or requency wave sway/time period damping reduction in sway resonance ampliication o sway Frequency and eriod natural period o vibration avoid resonance hard to predict seismic period aected by soil short period high stiness long period low stiness To ring the bell, the sexton must pull on the downswing o the bell in time with the natural requency o the bell. Mechanics o Materials 45 S2007abn Mechanics o Materials 46 S2007abn Design o Members beyond allowable stress... materials aren t uniorm 100% o the time ultimate strength or capacity to ailure may be dierent and some strengths hard to test or RISK & UNCERTINTY u u Factor o Saety accommodate uncertainty with a saety actor: ultimate load allowable load F. S with linear relation between load and stress: ultimate load ultimate stress F. S allowable load allowable stress Stress & Strain 29 Stress & Strain 30 13

14 oad and Resistance Factor Design loads on structures are not constant can be more inluential on ailure happen more or less oten UNCERTINTY R u D R D R R n - resistance actor - load actor or (D)ead & ()ive load Stress & Strain 31 S2005abn 14