LIED RCHITECTURL STRUCTURES: STRUCTURL NLYSIS ND SYSTEMS DR. NNE NICHOLS SRING 018 lecture two structural analysis (statics & mechanics) nalysis 1 pplied rchitectural Structures 009abn Structural Requirements serviceability strength delections eiciency economy o materials construction cost other nalysis www.pbs.org/wgbh/buildingbig/ 009abn Structure Requirements strength & equilibrium saety stresses not greater than strength adequate oundation Structure Requirements stability & stiness stability o components minimum delection and vibration adequate oundation nalysis 3 nalysis 4 1
Structure Requirements economy and construction minimum material standard sized members simple connections and details maintenance abrication/ erection Relation to rchitecture The geometry and arrangement o the load-bearing members, the use o materials, and the crating o joints all represent opportunities or buildings to epress themselves. The best buildings are not designed by architects who ater resolving the ormal and spatial issues, simply ask the structural engineer to make sure it doesn t all down. - Onouy & Kane nalysis 5 nalysis 6 Structural Loads - STTIC dead load static, ied, includes material weights, ied equipment live load transient and moving loads (including occupants) snow load Structural Loads STTIC & DYNMIC wind loads dynamic, wind pressures treated as lateral static loads on walls, pressure or suction pressure determined rom wind velocity, q h dynamic eects include motion rom bueting or vorte shedding W C d q h nalysis 7 nalysis 8
Structural Loads - DYNMIC earthquake loads seismic, movement o ground (3D) building mass responds static models oten used, V is static shear impact loads rapid, energy loads V ZICW R W Dynamic Response nalysis 9 nalysis 10 Dynamic Response period o vibration or requency wave sway/time period damping reduction in sway resonance ampliication o sway Statics & Mechanics Review how loads aect our structures statics: things don t move orces supports & connections equilibrium mechanics: things can change shape stress & strain delections buckling nalysis 11 nalysis 1 3
Structural Math quantiy environmental loads how big is it? evaluate geometry and angles where is it? what is the scale? what is the size in a particular direction? quantiy what happens in the structure how big are the internal orces? how big should the beam be? hysical Math physics takes observable phenomena and relates the measurement with rules: mathematical relationships need reerence rame measure o length, mass, time, direction, velocity, acceleration, work, heat, electricity, light calculations & geometry nalysis 13 nalysis 14 Units Vectors measures scalars any quantity US customary & SI vectors - quantities with direction like displacements Length Volume Mass orce Units Temperature in, t, mi gallon lb mass lb orce US SI mm, cm, m liter g, kg N, kn C summation results in the straight line path rom start to end normal vector is perpendicular to something y z nalysis 15 nalysis 16 4
orces & Reactions Newton s 3 rd law: or every orce o action there is an equal and opposite reaction along the same line eternal orces act on bodies can cause moments internal orces are in bodies between bodies (connections) nalysis 17 orce Components convenient to resolve into vectors at right angles in a nice coordinate system is between and rom cos y sin tan nalysis 18 y y y y y y Load Types weight ( = ma) W t concentrated distributed nalysis 19 uniorm linear riction =N w W W w 0 w W w W/ w W W/ Load Tracing tributary load w nalysis 0 think o water low concentrates load o area into center load w area tributary width width / / /3 /3 / /6 /3 5
Moments deined by magnitude and direction units: Nm, kt direction: + ccw (right hand rule) - cw C value ound rom B d and distance M d d also called lever or moment arm Equilibrium analytically R 0 R y y 0 M M 0 ree body diagrams nalysis 1 nalysis ree Body Diagram BD (sketch) tool to see all orces on a body or a point including eternal orces weights orce reactions eternal moments moment reactions internal orces Supports and Connections nalysis 3 nalysis 4 6
Supports and Connections Centroid average & y o an area or a volume o constant thickness W t where is weight/volume center o gravity = centroid o area nalysis 5 nalysis 6 y y I Moments o Inertia nd moment area math concept area (distance) need or behavior o beams columns I c d y Internal and in orces 3 equations per three-orce body two-orce body orces in line reactions per pin + support orces B G C E D y D nalysis 7 nalysis 8 7
Internal Beam V & M (+) maimums needed or design M ma at V = 0 Delected Shape V M + + - L L L/ +V +M positive bending moment tension in bottom, compression in top negative bending moment tension in top, compression in bottom zero bending moment inlection point nalysis 9 nalysis 30 Stress stress is a term or the intensity o a orce, like a pressure internal or applied orce per unit area stress Stress Types normal stress is normal to the cross section shear stress parallel to a surace v t or c td nalysis 31 nalysis 3 8
Stress Types bearing stress on a surace by contact in compression torsional stress by shear rom twisting nalysis 33 v T J p td v Bolt Stresses single shear double shear bearing nalysis 34 v d 4 p d 4 projected td Bending Stresses tension and compressive stress caused by bending shear stress rom bending VQ vave Ib nalysis 35 b Mc I M S Connectors Resisting Shear plates with nalysis 36 nails rivets bolts splices n connector y V VQ 4.43 4 y a longitudinal p I 8 1 connected area VQ I p p p p 9
Strain materials deorm aially loaded materials change length bending materials delect STRIN: nalysis 37 change in length over length strain L L roblem Solving 1. STTICS: equilibrium o eternal orces, internal orces, stresses. GEOMETRY: cross section properties, deormations and conditions o geometric it, strains 3. MTERIL ROERTIES: nalysis 38 stress-strain relationship or each material obtained rom testing Stress to Strain important to us in - diagrams: straight section LINER-ELSTIC recovers shape (no permanent deormation) E L E Behavior Types brittle semi-brittle nalysis 39 nalysis 40 10
lastic Behavior ductile at yield stress Maimum Stresses i we need to know where ma and v happen: 0 cos 1 ma o nalysis 41 nalysis 4 45 cos sin vma 0.5 o ma Thermal Deormation - the rate o strain per degree UNITS :, length change: thermal strain: C no stress when movement allowed T T L T T Beam Delections curvature, R 1 R y ma M EI M ( ) slope d EI ( ) curvature delection actual M ( ) EI M ( ) d EI allowable nalysis 43 nalysis 44 11
Column Stability short columns slenderness ratio = L e /r (L/d) radius o gyration = critical nalysis 45 critical critical Er actual r I E Le r L e a critical weak ais E Le r Column Stresses when a column gets stubby, y will limit the load real world has loads with eccentricity end conditions K L nalysis 46 L e 1