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E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS y S PRING 2018 x lecture two z loads, forces and vectors Forces 1 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Structural Design • planning • preliminary structural configuration • determination of loads • preliminary member selection • analysis • evaluation • design revision • final design Forces 2 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Structural Loads • STATIC and DYNAMIC • dead load – static, fixed, includes building weight, fixed equipment • live load – transient and moving loads (including occupants), snowfall Forces 3 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Structural Loads • wind loads – dynamic, wind pressures treated as lateral static loads on walls, up or down loads on roofs Forces 4 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Structural Loads • earthquake loads – seismic, movement of ground Forces 5 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Structural Loads • impact loads – rapid, energy loads Forces 6 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Forces • statics – physics of forces and reactions on bodies and systems – equilibrium (bodies at rest) • forces – something that exerts on an object: • motion • tension • compression Forces 7 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Forces • “action of one body on another that affects the state of motion or rest of the body” • Newton’s 3 rd law: – for every force of action there is an equal and opposite reaction along the same line http://www.physics.umd.edu Forces 8 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Force Vectors • applied at a point • magnitude – Imperial units: lb, k (kips) – SI units: N (newtons), kN • direction • sense (tail) (tip) Forces 9 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Forces on Rigid Bodies • for statics, the bodies are ideally rigid • can translate and rotate • internal forces are translate rotate – in bodies – between bodies (connections) • external forces act on bodies Forces 10 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Transmissibility • the force stays on the same line of action • truck can’t tell the difference = • only valid for EXTERNAL forces Forces 11 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Force System Types • collinear Forces 12 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Force System Types • coplanar Forces 13 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Force System Types • space Forces 14 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Adding Vectors • graphically – parallelogram law R • diagonal F • long for 3 or more vectors P – tip-to-tail • more convenient F R with lots of vectors P Forces 15 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Force Components • convenient to resolve into 2 vectors • at right angles • in a “nice” coordinate system F y •  is between F x and F from F x F y  x F x   F F cos F x F F y F y   F sin F y   F x 2 2 F x F F F x y F   y tan F Forces 16 Elements of Architectural Structures S2018abn x Lecture 2 ARCH 614

Trigonometry • F x is negative   – 90 to 270 Y 6 • F y is negative 5 4   Quadrant II Quadrant I – 180 to 360 3 2 • tan is positive 1 0 X -1 – quads I & III -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -2 -3 • tan is negative Quadrant III Quadrant IV -4 -5 – quads II & IV -6 Forces 17 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Component Addition • find all x components • find all y components • find sum of x components, R x (resultant) • find sum of y components, R y   2 2 R R R x y R P y R F y   y tan R y  P x R F x x R x Forces 18 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Alternative Trig for Components • doesn’t relate angle to axis direction •  is “small” angle between F and EITHER F x or F y • no sign out of calculator! • have to choose RIGHT F y trig function, resulting +/-? F y  direction (sign) and +/-? F x x component axis Forces 19 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Static Equilibrium • balanced & steady • no motion or translation • equilibrant opposite resultant X = X Forces 20 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Cables • simple • uses – suspension bridges – roof structures – transmission lines – guy wires, etc. • have same tension all along http:// nisee.berkeley.ed/ugodden • can’t stand compression Forces 21 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Cables Structures • use high-strength steel • need – towers – anchors • don’t want movement http:// nisee.berkeley.edu/godden Forces 22 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Cable Loads • straight line between forces • with one force – concurrent – symmetric Forces 23 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

Cable Loads • shape directly related to the distributed load • funicular Forces 24 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614

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 Forces 25 Elements of Architectural Structures S2018abn Lecture 2 ARCH 614