SS 3 (formulas)

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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
    • r=radius of gyration
    • Fa=allowable axial comp stress
  3. radius of gyration
    • 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
    • b=breadth
    • d'=actual depth of beam at the notch
    • d=total depth of beam
  6. horizontal shear stress

    • 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
    • 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
  9. deflection formula
    • =5wL4/384EI
    • wL=W
    • =5WL3/384EI
    • =KL3/EI

    • w=load per linear foot
    • W=total pounds
  10. horizontal thrust formula (arches)

    • H=horizontal thrust
    • w=total load
    • 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
  12. 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
  13. snow load reduction formula

    • 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
    for rectangle about centroid axis:  

    for rectangle about base:
  22. foundation pressure
    • F=foundation pressure
    • P=load on the foundation
    • A=area required for footing
  23. required column area
    required column area= concentric load/axial stress

    take  required
  24. expansion due to


    • 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
    • P=tensile load
    • L=original length
    • A=area
    • =deflection
  27. 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
  28. unit tensile stress
    unit stress =
  29. moment
    uniform load:   or   

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

    *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
  36. 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
  37. unit stress formula
    • f=P/A
    • f=unit stress
    • P=load
  38. area of a circle
  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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SS 3 (formulas)
2013-07-27 21:13:28

Structures Exam
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