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E LEMENTS OF A RCHITECTURAL S TRUCTURES : Structural Design F ORM, B EHAVIOR, AND D ESIGN ARCH 614 planning D R. A NNE N ICHOLS preliminary structural y S PRING 2019 configuration x determination of loads lecture two

  1. E LEMENTS OF A RCHITECTURAL S TRUCTURES : Structural Design F ORM, B EHAVIOR, AND D ESIGN ARCH 614 • planning D R. A NNE N ICHOLS • preliminary structural y S PRING 2019 configuration x • determination of loads lecture two • preliminary member selection z • analysis • evaluation loads, forces • design revision • final design and vectors Forces 1 Elements of Architectural Structures S2009abn Forces 5 Elements of Architectural Structures S2005abn Lecture 2 ARCH 614 Lecture 3 ARCH 614 Structural Loads Structural Loads • • STATIC and DYNAMIC wind loads • – dynamic, wind pressures treated as lateral dead load static loads on walls, up or down loads on – static, fixed, includes roofs building weight, fixed equipment • live load – transient and moving loads (including occupants), snowfall Forces 6 Elements of Architectural Structures S2005abn Forces 7 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 1

  2. Structural Loads Structural Loads • • earthquake loads impact loads – – seismic, movement of rapid, energy loads ground Forces 8 Elements of Architectural Structures S2005abn Forces 9 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 Forces Forces • statics • “action of one body on another that affects the state of motion or rest of the – physics of forces and reactions on bodies body” and systems • Newton’s 3 rd law: – equilibrium (bodies at rest) • forces – for every force of action there is an equal and – something that exerts on an object: opposite reaction along • motion the same line • tension • compression http:// nisee.berkeley.edu/godden Forces 11 Elements of Architectural Structures S2005abn Forces 10 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 2

  3. Force Vectors Forces on Rigid Bodies • applied at a point • for statics, the bodies are ideally rigid • magnitude • can translate and rotate – Imperial units: lb, k (kips) • internal forces are – SI units: N (newtons), kN translate rotate • direction – in bodies – between bodies (connections) • sense • external forces act on bodies (tail) (tip) Forces 12 Elements of Architectural Structures S2005abn Forces 13 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 Transmissibility Force System Types • the force stays on the same line of • collinear action • truck can’t tell the difference = • only valid for EXTERNAL forces Forces 14 Elements of Architectural Structures S2005abn Forces 15 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 3

  4. Force System Types Force System Types • coplanar • space Forces 13 Elements of Architectural Structures S2006abn Forces 17 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 Adding Vectors Force Components • convenient to resolve into 2 vectors • graphically • at right angles – parallelogram law R • diagonal • in a “ nice ” coordinate system F F y • long for 3 or more vectors •  is between F x and F from F x F y P  x F x   F F x F cos – tip-to-tail F F y F y   • more convenient F sin F y F R with lots of vectors   F x 2 2 F x F F F x y P F   y tan F Forces 19 Elements of Architectural Structures S2005abn x Forces 18 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 4

  5. Trigonometry Component Addition • find all x components • F x is negative   – 90 to 270 • find all y components Y 6 • F y is negative • find sum of x components, R x (resultant) 5 4   Quadrant II Quadrant I – 180 to 360 • find sum of y components, R y 3 2 • tan is positive 1 0 X   2 2 R R R -1 – quads I & III -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x y R -2 P y -3 • tan is negative Quadrant III Quadrant IV -4 R F y   y -5 tan R y  P x – quads II & IV -6 R F x x R x Forces 21 Elements of Architectural Structures S2005abn Forces 20 Elements of Architectural Structures S2005abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 Alternative Trig for Components Static Equilibrium • doesn ’ t relate angle to axis direction • balanced & steady •  is “ small ” angle between F and • no motion or translation EITHER F x or F y • equilibrant is opposite resultant • no sign out of calculator! X • have to choose RIGHT F y trig function, resulting +/-? F y  = direction (sign) and +/-? F x x component axis X Equilibrium 2 Elements of Architectural Structures S2006abn Forces 19 Elements of Architectural Structures S2006abn Lecture 5 ARCH 614 Lecture 3 ARCH 614 5

  6. Cables Cables Structures • simple • use high-strength steel • uses • need – suspension bridges – towers – roof structures – anchors – transmission lines • don’t want movement – guy wires, etc. • have same tension all along http:// nisee.berkeley.ed/ugodden • can’t stand compression http:// nisee.berkeley.edu/godden Equilibrium 29 Elements of Architectural Structures S2005abn Equilibrium 24 Elements of Architectural Structures S2006abn Lecture 5 ARCH 614 Lecture 5 ARCH 614 Cable Loads Cable Loads • straight line • shape directly between forces related to the • with one force distributed load • funicular – concurrent – symmetric Equilibrium 31 Elements of Architectural Structures S2005abn Equilibrium 32 Elements of Architectural Structures S2005abn Lecture 5 ARCH 614 Lecture 5 ARCH 614 6

  7. Cable Loads • trig: T x   T cos T y   T sin  • parabolic (catenary) – distributed uniform load 2 /   2 y y 4 h ( Lx x ) L h 2 4    h h L total L ( 1 8 32 ) L x 3 2 5 4 L L Equilibrium 33 Elements of Architectural Structures S2005abn Lecture 5 ARCH 614 7

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