# SS 3 (formulas)

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 Author: sabrinarusso ID: 227748 Filename: SS 3 (formulas) Updated: 2013-07-27 17:13:28 Tags: ARE Folders: Description: Structures Exam Show Answers:

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1. required area for wood beam for shear stress
2. allowable axial compressive stress formula
• Fa = Kl/r
• K=effective length
• l=unbraced length
• Fa=allowable axial comp stress
• term used in column design equal to
• I=moment of inertia of a member
• A=cross sectional area
4. unit shear stress formula (in a steel beam)

• fv=actual unit shear stress
• V=max vertical shear
• d=overall depth of abeam
• t=thickness of web
5. horizontal shear stress formula
• fv=3V/2bd X d/d'
• fv=horizontal shear stress
• V=shear force
• d'=actual depth of beam at the notch
• d=total depth of beam
6. 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
7. section modulus

M=bending moment
8. buckling tendency formula
• kl/r
• k=constant determined by fixity at ends
• *higher k - decreases column load capacity
• l=unbraced length of column
• -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
9. deflection formula
• =5wL4/384EI
• wL=W
• =5WL3/384EI
• =KL3/EI

• W=total pounds
10. horizontal thrust formula (arches)

• H=horizontal thrust
• L=length
• h=height
11. magnitude of hydrostatics pressure formula
magnitude of hydrostatic pressure=unit weight of liquid X depth

water unit weight=62.4 lbs/cubic ft
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

• S=total snow load in lbs/sf
• *reduce snow load for pitch ovre 20degree and exceeds snow load of 20psf
14. required width of footing (wall footing)
required width of footing = total load/bearing soil capacity
15. required area of footing formula (single column footing)
required area of footing = total load (include weight of footing)/bearing capacity of soil
16. throat area formula
throat area = 0.707 x weld size
17. allowable load per in of weld formula
allowable load per in of weld=allowable stress X throat area
18. retaining wall base pressure formula
base pressure = equivalent fluid pressure X height
19. retaining wall total earth pressure formula
total earth pressure=base pressure X height/2
20. 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
21. moment of inertia

22. foundation pressure
• F=foundation pressure
• A=area required for footing
23. required column area
required column area= concentric load/axial stress

take  required
24. expansion due to
or

or

• P/A=internal stress
• n=coefficient of expansion
• E=modulous of elasticity
• =change in temperature
25. section modulus
• 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
26. modulus of elasticity (E)
• *ratio of unit stress to unit strain
• L=original length
• A=area
• =deflection
27. deflection formula

• E=modulus of elasticity
• I=moment of inertia
• L=original length
• *to reduce deflection, increase I
28. unit tensile stress
unit stress =
29. moment

*max moment when shear diagram crosses 0
30. 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
31. formula to calculate deflection change when temperature change

• = deflection
• n = coefficient of expansion (steel=0.0000065)
• L = original length
• t = temperature change
32. max bending moment formula
• Fb=M/S
• M=FbS
• M=max moment
• Fb=fiber stress in bending
• S=section modulus
33. 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
34. 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
35. max shear formula

V=max shear
• f=P/A or A=P/f
• A=foundation load/allowable soil bearing pressure
• A=footing area
• f=allowable soil bearing pressure
• =(x)(x)
• x= dimension
37. unit stress formula
• f=P/A
• f=unit stress
38. area of a circle
r2
39. triangle formulas

40. moment capacity formula
• Mu=moment capacity
• As=cross sectional area of tensile reinforcement in si
• fy=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
41. unit strain formula

• =unit strain
• =total strain
• L=original length
42. internal stress formula

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

• f=flexural stress
• M=bending moment
• =distance from the neutral axis to the fiber under consideration
• I=moment of inertia
44. finding beam size
given: 30ft span
A36 steel
P40 (use from reference)
• 1) max moment = wL2/8=1800x302/8=202,500ft-lbsx12=2,430,000in-lbs
• 2) S=M/Fb=2,430,000/24,000=101.25in3
• Fb for ASTM A36=24,000psi
• 3) use chart P40 to find S section
45. 20ft span:
25ft span:
• (244)/(20)4=2.44
• 0.50x2.44=1.22"
46. parapet calculations
• when parapet is at the roof of the building
47. calculating size of a I-beam
1) calculate  or

2) calculate:

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

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