SS 3 (formulas)
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required area for wood beam for shear stress

allowable axial compressive stress formula
 F_{a} = Kl/r
 K=effective length
 l=unbraced length
 r=radius of gyration
 F_{a}=allowable axial comp stress

radius of gyration
 term used in column design equal to
 I=moment of inertia of a member
 A=cross sectional area

unit shear stress formula (in a steel beam)
 f_{v}=actual unit shear stress
 V=max vertical shear
 d=overall depth of abeam
 t=thickness of web

horizontal shear stress formula
 f_{v}=3V/2bd X d/d'
 f_{v}=horizontal shear stress
 V=shear force
 b=breadth
 d'=actual depth of beam at the notch
 d=total depth of beam

horizontal shear stress
or
 v=horizontal shear
 V=vertical shear at section under consideration
 Q=statistical moment about the neutral axis of the area above the plane under consideration

section modulus
M=bending moment

buckling tendency formula
 kl/r
 k=constant determined by fixity at ends
 *higher k  decreases column load capacity
 l=unbraced length of column
 r=radius of gyration
 ratio of a measure of the buckling tendency of a steel column
 larger the value of kl/r, greater tendency of a column to buckle, resulting in lower column capacity


horizontal thrust formula (arches)
 H=horizontal thrust
 w=total load
 L=length
 h=height

magnitude of hydrostatics pressure formula
magnitude of hydrostatic pressure=unit weight of liquid X depth
water unit weight=62.4 lbs/cubic ft

retained earth loads formulas
1)pressure at bottom of wall
2)total pressure
1)pressure at bottom of wall=height X unit weight of equivalent fluid
2)total pressure=pressure at bottom/2 X height of wall

snow load reduction formula
 S=total snow load in lbs/sf
 *reduce snow load for pitch ovre 20degree and exceeds snow load of 20psf

required width of footing (wall footing)
required width of footing = total load/bearing soil capacity

required area of footing formula (single column footing)
required area of footing = total load (include weight of footing)/bearing capacity of soil

throat area formula
throat area = 0.707 x weld size

allowable load per in of weld formula
allowable load per in of weld=allowable stress X throat area

retaining wall base pressure formula
base pressure = equivalent fluid pressure X height

retaining wall total earth pressure formula
total earth pressure=base pressure X height/2

retaining wall bending moment at base formula
bending moment at base = total earth pressure X
 retain wall = height/3 *distance from centroid of triangle to base
 basement = height/2

moment of inertia
for rectangle about centroid axis:
for rectangle about base:

foundation pressure
 F=foundation pressure
 P=load on the foundation
 A=area required for footing

required column area
required column area= concentric load/axial stress
take
required

expansion due to



deflection formula
 K=constant that depends on the load and loading condition
 E=modulus of elasticity
 I=moment of inertia
 L=original length
 *to reduce deflection, increase I

unit tensile stress
unit stress =

moment
uniform load:
or
 w=load in lbs/ft
 simple load with concentrated load:
*max moment when shear diagram crosses 0

finding required column size using formula 0.30(E)/(I/d)^{2}
*where E is given
 trial and error:
 1)test=0.3(E)/(I/d)^{2} to find allowable stress
 2)to find required column area=axial load/allowable stress=x
 3)see if x is adequate to match column areas given

formula to calculate deflection change when temperature change
 = deflection
 n = coefficient of expansion (steel=0.0000065)
 L = original length
 t = temperature change

max bending moment formula
 F_{b}=M/S
 M=F_{b}S
 M=max moment
 F_{b}=fiber stress in bending
 S=section modulus

factor of safety
 factor of safety=(total vertical load X coefficient of friction)/(earth pressure/2)Xh
 *ratio of the ultimate strength of a material to its working stress

formula for finding the bearing pressure under the base plate
*given length of column, axial load, area/size of base plate
 F=P/A=axial load/area of bearing plate
 F=bearing pressure

max shear formula
V=max shear

calculating pad footing
given dead load and live load, soil bearing value
 f=P/A or A=P/f
 A=foundation load/allowable soil bearing pressure
 A=footing area
 P=foundation load
 f=allowable soil bearing pressure
 =(x)(x)
 x= dimension


area of a circle
r
^{2}





flexure formula
 f=flexural stress
 M=bending moment
 =distance from the neutral axis to the fiber under consideration
 I=moment of inertia

finding beam size
given: 30ft span
load=1800lbs/ft
A36 steel
P40 (use from reference)
 1) max moment = wL^{2}/8=1800x30^{2}/8=202,500ftlbsx12=2,430,000inlbs
 2) S=M/F_{b}=2,430,000/24,000=101.25in^{3}
 F_{b} for ASTM A36=24,000psi
 3) use chart P40 to find S section

20ft span:
25ft span:
 (24^{4})/(20)^{4}=2.44
 0.50x2.44=1.22"

parapet calculations
 when parapet is at the roof of the building

calculating size of a Ibeam
1) calculate
or
2) calculate:
 Z=required plastic section modulus
 m=max. moment=wL^{2}/8
 =1.67
 3) section modulus on chart