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

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1 RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SUMMER 2014 Mechanics o Materials MECHNICS MTERIS lecture ive mechanics o materials Mechanics o Materials 1 rchitectural Structures F2009abn Mechanics o Materials 2 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 3 Mechanics o Materials 4 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 5 Mechanics o Materials 6 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 7 Mechanics o Materials 8 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 (direct) normal stress is normal to the cross section stressed area is perpendicular to the load t or c Mechanics o Materials 9 Mechanics o Materials 10 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 11 Mechanics o Materials 12 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 13 Mechanics o Materials 14 Structures and Shear what structural elements see shear? beams bolts connections splices slabs ootings walls wind seismic loads V Bolts connected members in tension cause shear stress connected members in compression cause bearing stress Mechanics o Materials 15 Mechanics o Materials 16 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 4 v d Mechanics o Materials 18 4 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 + UNITESS strain Mechanics o Materials 19 Mechanics o Materials 20 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) Mechanics o Materials 21 Mechanics o Materials 22 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 Fir vs. steel? Mechanics o Materials 23 Mechanics o Materials 24 6

7 Behavior Types ductile - necking true stress engineering stress (simpliied) o Behavior Types brittle semi-brittle Mechanics o Materials 25 Mechanics o Materials 26 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 Mechanics o Materials 27 Mechanics o Materials 28 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 Mechanics o Materials 29 Mechanics o Materials 30 Elastic, lastic, Fatigue elastic springs back plastic has permanent deormation atigue caused by reversed loading cycles lastic Behavior ductile at yield stress Mechanics o Materials 31 Mechanics o Materials 32 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 Mechanics o Materials 33 Mechanics o Materials 34 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 Mechanics o Materials 35 Mechanics o Materials 36 9

10 Stress Concentrations why we use ave increase in stress at changes in geometry sharp notches holes corners Maximum Stresses i we need to know where max and v happen: 0 cos 1 max F o Mechanics o Materials cos sin Mechanics o Materials 38 vmax o 2 max Maximum Stresses Deormation Relationships physical movement axially (same or zero) rotations rom axial changes 20 kn aluminum steel E relates to Mechanics o Materials 39 Mechanics o Materials 40 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 Mechanics o Materials 41 Mechanics o Materials 42 Coeicients o Thermal Expansion Wood Glass Steel Wrought Iron Copper Bronze Brass Material Concrete Cast Iron luminum Mechanics o Materials 43 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 Mechanics o Materials 44 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 Mechanics o Materials 45 Mechanics o Materials 46 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 Mechanics o Materials 47 Mechanics o Materials 48 12

13 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 Mechanics o Materials 49 13