WIND FORCES

wind load

Wind Load is an ‘Area Load’ (measured in PSF) which loads the surface area of a structure.

SEISMIC FORCES

seismic load

Seismic Load is generated by the inertia of the mass of the structure : VBASE

Redistributed (based on relative height and weight) to each level as a ‘Point Load’ at the center of mass of each floor level: FX

VBASE wx hx

(w h)

( VBASE )

(Cs)(W)VBASE =

Fx =

Where are we going with all of this?

global stability & load flow (Project 1) tension, compression, continuity

equilibrium: forces act on rigid bodies,and they don’t noticeably move

boundary conditions: fixed, pin, roller idealize member supports & connections

external forces: are applied to beams & columns as concentrated & uniform loads

categories of external loading: DL, LL, W, E, S, H (fluid pressure)

internal forces: axial, shear, bending/flexure

internal stresses: tension, compression, shear, bending stress,

stability, slenderness, and allowable compression stress

member sizing for flexure

member sizing for combined flexure and axial stress (Proj. 2)

Trusses (Proj. 3)

EXTERNAL FORCES

( + ) M1 = 00= -200 lb(10 ft) + RY2(15 ft)

RY2(15 ft) = 2000 lb-ft

RY2 = 133 lb

( +) FY = 0

RY1 + RY2 - 200 lb = 0

RY1 + 133 lb - 200 lb = 0

RY1 = 67 lb

( +) FX = 0

RX1 = 0

RY1

200 lb

RY2

RX1

10 ft 5 ft

67 lb

200 lb

0 lb

10 ft 5 ft 133 lb

= 880lb/ft

RY224 ft RY1

RX1

RY224 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

RY1

RX1

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0 RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

( +) FY = 0

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

( +) FY = 0

RY1 + RY2 – 21,120 lb = 0

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

( +) FY = 0

RY1 + RY2 – 21,120 lb = 0

RY1 + 10,560 lb – 21,120 lb = 0

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

( +) FY = 0

RY1 + RY2 – 21,120 lb = 0

RY1 + 10,560 lb – 21,120 lb = 0

RY1 = 10,560 lb

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

( +) FY = 0

RY1 + RY2 – 21,120 lb = 0

RY1 + 10,560 lb – 21,120 lb = 0

RY1 = 10,560 lb

( +) FX = 0

RX1 = 0

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

( + ) M1 = 0–21,120 lb(12 ft) + RY2(24 ft) = 0

RY2(24 ft) = 253,440 lb-ft

RY2 = 10,560 lb

( +) FY = 0

RY1 + RY2 – 21,120 lb = 0

RY1 + 10,560 lb – 21,120 lb = 0

RY1 = 10,560 lb

( +) FX = 0

RX1 = 0

= 880 lb/ft

24 ft 10,560 lb

0 lb

10,560 lb

RY1 RY2

RX1

24 ft

resultant force - equivalent total load that is a result of a distributed line load

resultant force = area loading diagram

resultant force = ( L)

= 880 lb/ft(24ft) = 21,120 lb12 ft 12 ft

SIGN CONVENTIONS(often confusing, can be frustrating)

External – for solving reactions(Applied Loading & Support Reactions)

+ X pos. to right - X to left neg.+ Y pos. up - Y down neg+ Rotation pos. counter-clockwise - CW rot. neg.

Internal – for P V M diagrams(Axial, Shear, and Moment inside members)Axial Tension (elongation) pos. | Axial Compression (shortening) neg.Shear Force (spin clockwise) pos. | Shear Force (spin CCW) neg.Bending Moment (smiling) pos. | Bending Moment (frowning) neg.

STRUCTURAL ANALYSIS:

INTERNAL FORCES

P V M

INTERNAL FORCES

Axial (P)

Shear (V)

Moment (M)

V

+P + +

M

V

- -

M

-P

RULES FOR CREATING P DIAGRAMS

1. concentrated axial load | reaction = jump in the axial diagram

2. value of distributed axial loading = slope of axial diagram

3. sum of distributed axial loading = change in axial diagram

-10k

-10k

+20k

- 0 +

-20k 0 compression

-10k

-20k

-10k

-10k

+20k

RULES FOR CREATING V M DIAGRAMS (3/6)

1. a concentrated load | reaction = a jump in the shear diagram

2. the value of loading diagram = the slope of shear diagram

3. the area of loading diagram = the change in shear diagram

= - 880 lb/ft

24 ft

+10.56k

0 lb

10,560 lb

P

V

Area of Loading Diagram

-0.88k/ft * 24ft = -21.12k

10.56k + -21.12k = -10.56k

-10.56k

0 0

0 0

-880 plf = slope

10,560 lb

RULES FOR CREATING V M DIAGRAMS, Cont. (6/6)

4. a concentrated moment = a jump in the moment diagram

5. the value of shear diagram = the slope of moment diagram

6. the area of shear diagram = the change in moment diagram

= - 880 lb/ft

24 ft

+10.56k

0 lb

10,560 lb

P

V

M

Area of Loading Diagram

-0.88k/ft * 24ft = -21.12k

10.56k + -21.12k = -10.56k

-10.56k

0 0

0 0

-880 plf = slope

10,560 lb

0 0

Slope initial = +10.56k

Area of Shear Diagram

(10.56k )(12ft ) 0.5 = 63.36 k-ft

pos.

slope

zero slope 63.36k’ neg. slope

(-10.56k)(12ft)(0.5) = -63.36 k-ft

W2 = 30 PSF

W1 = 20 PSF

Wind Loading

W2 = 30 PSF

W1 = 20 PSF

1/2 LOAD

SPAN

SPAN

1/2 LOAD

1/2 +

1/2 LOAD

Wind Load spans to each level

10 ft

10 ft

roof= (30 PSF)(5 FT)

= 150 PLF

Total Wind Load to roof level

second= (30 PSF)(5 FT) + (20 PSF)(5 FT)

= 250 PLF

Total Wind Load to second floor level

second= 250 PLF

roof= 150 PLF

seismic load

Seismic Load is generated by the inertia of the mass of the structure : VBASE

Redistributed (based on relative height and weight) to each level as a ‘Point Load’ at the center of mass of the structure or element in question : FX

VBASE wx hx

(w h)

( VBASE )

(Cs)(W)VBASE =

Fx =

Total Seismic Loading :

VBASE = 0.3 W

W = Wroof + Wsecond

wroof

wsecond flr

W = wroof + wsecond flr

VBASE

Redistribute Total Seismic Load to each level based on relative height and weight

Fx =

Froof

Fsecond flr

VBASE (wx) (hx)

(w h)

Load Flow to Lateral Resisting System :

Distribution based on Relative Rigidity

Assume Relative Rigidity :

Single Bay MF :Rel Rigidity = 1

2 - Bay MF :Rel Rigidity = 2

3 - Bay MF :Rel Rigidity = 3

Distribution based on Relative Rigidity :

R = 1+1+1+1 = 4

Px = ( Rx / R ) (Ptotal)

PMF1 = 1/4 Ptotal