Appendix B â Analysis formulae (1/8). THIS DOCUMENT IS COPYRIGHT AND IS ... B.4 Vibration. Typically for most structures Where: f is in cycles per second.
APPENDIX B – ANALYSIS FORMULAE B.1 Elastic bending formulae Bending about a principle axis:
σ M = = Eκ ; y I
curvature-change
κ=
1 1 − R R0
In general, bending moment is section modulus Z times maximum bending stress. Longitudinal shear force S on material of area As , due to transverse shear force F on the beam.
S=
F I
∫
AS
y dA =
F AS y I
per unit length of beam.
B.2 Elastic torsion formulae Round shafts:
τ T = = Gφ r J
where φis the angle of twist per unit length
∫
2 and J = r dA is the polar moment of area.
Circular area, radius R: J =
π R4 2
Thin circular tube, radius R thickness t: J = 2π R 3 t
Thin walled tube of arbitrary cross-section: τ=
T 2 Ae t
:
T =G
4 Ae2 φ ds ∫t
where Ae is the enclosed area to mid thickness, t is the wall thickness. and s is the distance round the permiter.
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
Appendix B – Analysis formulae (2/8)
B.3 Taut wires, cables or chains Uniformly loaded cables with horizontal chords
s = span length f = cable sag n = f/s = sag ratio L = length of cable curve ∆Ls = cable elongation due to axial stress ∆Lt = cable elongation due to temperature change, t A = area of cable E = modulus of elasticity of cable ε = thermal coefficient of linear expansion t = temperature change in °F p = load per unit length
Uniformly loaded cables With inclined chords
(
4f a. y = 2 sx − x 2 s b. H = ps 2 / 8 f
a. y = b. H =
e. ∆L s ≅
8 3
n2 −
Hs
16
AE
3
1 +
f =
18 y
2
n2 8 3
n2
18 d . L = s1 + n 2 − 18n 4 + ... 5 Hs 36 2 e. ∆Ls ≅ 1 + n AE 5
Hs 16n 2 1 + sec θ AE 3 sec 4 θ
18 f . ∆Lt ≅ εts1 + n 2 5
sec θ
for most structures
n 4 + ...
c. Tmax = 1 + 36n 2
Where: f is in cycles per second y is the static deflection in mm
Simply supported Mass concentrated in centre
f =
15.8
Simply Supported Mass and stiffness distributed
f =
18
Cantilever Mass concentrated at end
Cantilever Mass and stiffness distributed
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
5
x3 a. y = f 1 − 8 3 s b. H = ps 2 / 24 f
B.4 Vibration Typically
32
f . ∆Lt = εtL ≅ εts1 +
sec θ
8n f . ∆Lt ≅ εts1 + 3 sec 4 θ Hh ps + g . Vs = s 2
8f
Triangular loading on cables with horizontal chords
2
ps 2
d . L = s1 +
h c. Tmax = H 1 + + 4n s
e. ∆Ls ≅
2
s2
c. Tmax = H 1 + 16n 2
)
8n 2 d . L ≅ s1 + 3 sec 4 θ
(sx − x )
4f
f =
y
y
15.8
f =
y
19.7 y
Appendix B – Analysis formulae (3/8)
B.5 Design formulae for beams - cantilever
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
Appendix B – Analysis formulae (4/8)
B.6 Design formulae for beams - fixed both ends
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
Appendix B – Analysis formulae (5/8)
B.7 Design formulae for beams - simply supported
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
Appendix B – Analysis formulae (6/8) [B.7 Design formulae for beams - simply supported (cont..)]
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
Appendix B – Analysis formulae (7/8)
B.8 Design formulae for beams - propped cantilever
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
Ver 3.0 / Aug 98
Appendix B – Analysis formulae (8/8) [B.8 Design formulae for beams - propped cantilever (cont..)]
THIS DOCUMENT IS COPYRIGHT AND IS PUBLISHED FOR DISTRIBUTION ONLY WITHIN THE OVE ARUP PARTNERSHIP. IT IS NOT INTENDED FOR AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY.
10.07m fully retracted. 10.07m to. 12.50m. 12.50m to. 15.00m. 15.00m to. 17.50m. 17.50m to. 20.00m. 20.00m to. 22.50m. 22.50m to. 24.57m. 3.0m. 25.40. 20.70.
3.00. 3.00. 3.00. 3.22. 3.22. 3.22. 3.22. 3.51. 3.51. 3.51. 3.51. 120. 2.82. 2.82 .... Decking is manufactured from material meeting the following specification: BS EN 10147 ... accordance with guidance given in SCI publication 056-'The fire resistan
Greater of 25 or bar diameter. Waterstops / waterbars. ⢠Required by BS 8102 for grade 1 basements with concrete design to BS 8110. ⢠Give extra "comfort" at ...
Minimum periods (hours) for elements of structure in a: Basement storey(!) Ground or ... CONCRETE. For cover details, see Section 4.2 Reinforced Concrete ...
plus the overall load of the complete structure as well as the loading of an ... It is important that all foundation designs are reviewed by a geotechnical engineer -.
If at the top of a ramp steeper than 1 in 10 the floor or roof is laid to a fall of 1 in 60 or steeper away from the ramp, a transition length should be provided.
When used with flexural strength in parallel direction, assume the orthogonal ratio ... joint (acoustic and thermal insulation, weathertightness, fire separation, etc).
p is the limiting unfactored stress in shear v. Note : A material factor up to ... For durability see corrosion protection table below. ... Young's modulus. 70 kN/mm2.
Rev A. 22 Feb 1999, units for load at the end of 3.4 corrected. 3.1 .... IStructE & ICE, Manual for the design of reinforced concrete building structures ("Green.
There are eight steps required to complete the structural design. First, you need to determine the overall load factors, then estimate the resulting external loads.
oriented user of multigrid methods in large-scale applications in the engineering sciences. ... of usually smaller dimension Nj (N1 + . . . + NJ N). Note that in some ...
The Preferences Panel is accessed from the File menu: File:Preferences. ..... Tip: If you unselect all objects (choose None in the name drop-down box), the ...
of lightweight concrete can be computed using the same formula as normal concrete. ..... (50.27) where a can be calculated by means of the quadratic equation.
Calculate the forces at work to maximize ... airplane's structure and work out all the .... having the correct angle is vital in .... This triangle can then be used. RPM.
of structural steel design for fire protection, refer to the latest edition of AISI ... Columns, and Designing Fire Protection for Steel Trusses as well as in the Uniform.
The equilibrium market condition for the foreign good is such that foreign ..... there are unemployed workers (1 â N) who spend e hours searching for a job.
The ability to manipulate complex numbers is very handy in circuit anal- ysis and in electrical engineering in general. Complex numbers are par- ticularly useful ...
26 août 2013 - $3.50 m2. 13. $1.50 Roll. Installment. Remarks: All prices are in US Dollars. Rock. #4 Rebar. Gravel ... Subtotal. 20% Contingency. White Sand ...