SS 3 (formulas)

• F_a = Kl/r
• K=effective length
• l=unbraced length
• r=radius of gyration
• F_a=allowable axial comp stress

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

• f_v=actual unit shear stress
• V=max vertical shear
• d=overall depth of abeam
• t=thickness of web

• 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

  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

M=bending moment

• 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

• =5wL⁴/384EI
• wL=W
• =5WL³/384EI
• =KL³/EI

• w=load per linear foot
• W=total pounds

• H=horizontal thrust
• w=total load
• L=length
• h=height

magnitude of hydrostatic pressure=unit weight of liquid X depth

water unit weight=62.4 lbs/cubic ft

1)pressure at bottom of wall=height X unit weight of equivalent fluid

2)total pressure=pressure at bottom/2 X height of wall

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

required width of footing = total load/bearing soil capacity

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

throat area = 0.707 x weld size

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

base pressure = equivalent fluid pressure X height

total earth pressure=base pressure X height/2

bending moment at base = total earth pressure X

• retain wall = height/3 *distance from centroid of triangle to base
• basement = height/2 

for rectangle about centroid axis:  

for rectangle about base:

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

required column area= concentric load/axial stress

take  required

 or   


 or      

• P/A=internal stress
• n=coefficient of expansion
• E=modulous of elasticity
• =change in temperature

• ratio of the moment of inertia of a beam (I) to the distance from its neutral axis to the most remote fiber (c)
•   *for I-beam:

 

• f=flexural (bending) stress
• M=bending moment

• 
• 
• *ratio of unit stress to unit strain
• P=tensile load
• L=original length
• A=area
• =deflection

• 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 stress =

uniform load:   or   

• w=load in lbs/ft
• simple load with concentrated load:  

*max moment when shear diagram crosses 0

• 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

• = deflection
• n = coefficient of expansion (steel=0.0000065)
• L = original length
• t = temperature change

• F_b=M/S
• M=F_bS
• M=max moment
• F_b=fiber stress in bending
• S=section modulus

• 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

• F=P/A=axial load/area of bearing plate
• F=bearing pressure

V=max shear

• 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

• f=P/A
• f=unit stress
• P=load

r²

• 
• M_u=moment capacity
• A_s=cross sectional area of tensile reinforcement in si
• f_y=specified yield strength of reinforcement
• d=distance from extreme compression fiber to centroid
• a=depth of rect stress block
• =strength reduction factor
• =0.90 for flexure =0.75 spiral col = 0.90 for reinforced conc beam = 0.85 for shear=0.70 tied column

• =unit strain
• =total strain
• L=original length

• n(steel)=0.0000065
• P/A=internal stress
• n=coefficient of thermal expansion
• t=temperature change
• =change in length

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

• 1) max moment = wL²/8=1800x30²/8=202,500ft-lbsx12=2,430,000in-lbs
• 2) S=M/F_b=2,430,000/24,000=101.25in³
• F_b for ASTM A36=24,000psi
• 3) use chart P40 to find S section

• (24⁴)/(20)⁴=2.44
• 0.50x2.44=1.22"

• 
• when parapet is at the roof of the building

1) calculate  or

2) calculate:

• Z=required plastic section modulus
• m=max. moment=wL²/8
• =1.67
• 3) section modulus on chart