two loads, forces and vectors ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2017 lecture ARCH 614

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1 ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2017 lecture two y x z loads, forces and vectors Forces 1

2 Structural Design planning preliminary structural configuration determination of loads preliminary member selection analysis evaluation design revision final design Forces 2

3 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

4 Structural Loads wind loads dynamic, wind pressures treated as lateral static loads on walls, up or down loads on roofs Forces 4

5 Structural Loads earthquake loads seismic, movement of ground Forces 5

6 Structural Loads impact loads rapid, energy loads Forces 6

7 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

8 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 Forces 8

9 Force Vectors applied at a point magnitude Imperial units: lb, k (kips) SI units: N (newtons), kn direction sense (tail) (tip) Forces 9

10 Forces on Rigid Bodies for statics, the bodies are ideally rigid can translate and rotate internal forces are in bodies translate between bodies (connections) external forces act on bodies rotate Forces 10

11 Transmissibility the force stays on the same line of action truck can t tell the difference = only valid for EXTERNAL forces Forces 11

12 Force System Types collinear Forces 12

13 Force System Types coplanar Forces 13

14 Force System Types space Forces 14

15 Adding Vectors graphically parallelogram law diagonal long for 3 or more vectors F R P tip-to-tail more convenient with lots of vectors R F P Forces 15

16 Force Components convenient to resolve into 2 vectors at right angles in a nice coordinate system y F is between F x and F from F x F x F y F Forces 16 tan F cos F sin 2 2 F x F y F F y x F y F F x F F y F y F x F x x

17 Trigonometry F x is negative 90 to 270 F y is negative 180 to 360 tan is positive quads I & III tan is negative quads II & IV -6 Y Quadrant II 3 Quadrant I Quadrant IV -5 Quadrant III X Forces 17

18 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 R 2 2 R x R y R tan R R y x P y R y F y F x R x P x Forces 18

19 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 trig function, resulting direction (sign) and component axis +/-? F x F x y +/-? F y Forces 19

20 Static Equilibrium balanced & steady no motion or translation equilibrant opposite resultant X = X Forces 20

21 Cables simple uses suspension bridges roof structures transmission lines guy wires, etc. have same tension all along can t stand compression nisee.berkeley.ed/ugodden Forces 21

22 Cables Structures use high-strength steel need towers anchors don t want movement nisee.berkeley.edu/godden Forces 22

23 Cable Loads straight line between forces with one force concurrent symmetric Forces 23

24 Cable Loads shape directly related to the distributed load funicular Forces 24

25 Cable Loads trig: T T cos x T T sin y parabolic (catenary) distributed uniform load y 4h( Lx x ) / L 2 L h 4 32 total 5 4 L( 1 8 h 3 L L ) x y L h Forces 25

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