DESIGN CALCULATION

FOR

DOME STRUCTURE – TYPE 1

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DESIGN CALCULATIONS FOR THE DOME STRUCTURE – TYPE 1

I. General1. Design Philosophy

The purpose of this calculation is to design the dome structure for its integrity, strength and stability verification. The result of this conclusion is that the structure considered adequate in meeting the required of design criteria.

2. Unit of Measurement

Unit of measurement in design shall be in Metric system.

II. Design Calculations1. Design Code and reference:

BS 5950 1190: Structural use of steel work in buildingChapter V. Loading part 2 – Wind loadsSTAAD PRO – Structural Program for calculations.Uniform Building Code – 1982 Edition

2. Materials

Main Beam – Aluminium Tubes 100X50X3 mm th.The modulus of elasticity of Aluminium E = 70000 N/mm2

Ultimate Bending stress – Po - σ = 165 N/mm2

Ultimate Tensile Stress – Pa = 130 N/mm2

Ultimate Shear Stress – Pv = 65 N/mm2

Co-efficient of Linear Expansion (α) = 23 X 10-6 / 0 C

3. Loading

Dead Load – Self weight is consideredDead Load of Glass panels assumed as 100 Kg/m2

Additional Point load of 100 Kgs = 1 KN shall be placed at the centre of dome.

Live load - 0.6 KN/m2

Wind loads (WL) calculated as per CP3: ch.V

The dome structure is located at a height of 15.0m.

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Basic wind speed assumed as 45 m/s.

Basic wind speed V = 45.0 m/sec

Design wind speed Vs = V x S1 x S2 x S3

Where,

Topography factor, S1 = 1.0

For the calculation of S2, ground roughness, building size and height above ground, factor S2 = 0.95, as per CP3: Chapter V: Part 2, Clause 1 (Open country with no obstructions), class B for 4m average height.

Statistical factor, S3 = 1.0

Design wind speed Vs = 45.0 x 1.0 x 0.95 x 1.0

Design wind speed Vs = 42.75 m/sec

Wind pressure q = k Vs2

K – constant = 0.613

Wind pressure q = 0.613 x (42.75)2

Wind pressure q = 1120 N/m2 or 1.12 KN/m2

The maximum and minimum pressure co-efficients are, Cp = +0.7, and -1.0,

Net wind Pressure = Cp X q

Net wind Pressure q = -1.0 x 1.12 = -1.12 KN/m2

4. Load Combinations

Design & Ultimate factors are considered.

as per BS standard,

UL = 1.4 DL + 1.6 LL

UL = 1.2 DL + 1.2 LL + 1.2 WL

UL = 1.0 DL + 0.8 LL + 0.8 WL – Deflection Check

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5. Design Method

The dome structure with a diameter 6.40m and a height of 3.20m is considered and as shown and the spacing between each truss is considered in radial at an angle of 30º and the distance at the end of the bays.

Loads are calculated on the spacing between the structures which are as follows:

Dead Loads:a) Self Weight to be checked from the programb) Dead load of 100 Kg/m2 of the glass panels is calculated as

1.0 X 1.50 = 1.50 KN/m

Vertical Point Load of 1.0 KN

Live Loads – 0.6 X 1.50 = 0.90 KN/m

Wind Loads:

a) Downward wind load = 1.12 X 1.50 = 1.68 KN/m

To check the dome structure against all the above loading combination and to be on factor of safety (see attached calculations made by the structural program STAADPRO).

COMPUTATION OF MAXIMUM BENDING MOMENT

The Glass panels are of size 900mm X 1500mm.

Hence, Maximum clear span of Glass Panel is considered as 1.50 m as per shop drawings.

Maximum wind load of Glass = 0.90 x 1.120

Maximum wind load on Glass = 1.008 KN/m

B.M (max) = w l2 /8

B.M (max) = 1.008 X (1.50)2 /8

B.M (max) = 0.2835 KNm

Calculation of Actual Bending Stress (Fb)

Fb = M / Z

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Z = Sectional Modulus

Z = bd2 / 6 where as d=13.14mm b = 1000mm

Z = 28,776.6 mm3

Fb = 315,000 / 28,776.60

Fb = 10.95 N/mm2 which is greater than the 56 N/mm2

The Actual Bending Stress is less than the Allowable Bending Stress, Hence, the section is Safe.

Check for Deflection:

δ = 5 WL4 / (384 EI)

δ < L / 375 or 19mm which ever is less

E = 72000 MPa

I = bd3 / 12 where as d=13.14mm b = 1000mm

I xx = 189,062.26 mm4

δ = 5 X (0.8*1.008 X 1.50 X 1000) X (1500)3 /(384 X 72000 X 189,062.26)

δ = 3.906mm

L/375 = 1500 / 375

L/375 = 4mm (Permissible deflection)

δ < 4mm

Hence the deflection is less than the permissible value, and safe against deflection.

CONNECTION DESIGN AT BASE – DETAIL E

Maximum Force as per the STAAD output:

Fx = 11.12 KN,

Fy = 23.05 KN &

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Fz = 0 KN

Check for Bolt:

Capacity of M16 bolts = (π/4) X (16)2 X 0.78 X 375 / 1000

Capacity of M16 bolt is 58.8 KN

Capacity of 2 No.’s M16 Bolt is 117.6 KN

The Resultant force acting on the surface of the bolt should be less than the capacities of the bolt used.

Resultant Force = F =SQRT (Fy2 + F12)

Where as F1 = SQRT (Fx2 + Fz2)

F1 = SQRT (11.122 + (0)2)

F1 = SQRT (123.65 + 0)

F1 = SQRT (123.65)

F1 = 11.12 KN

Resultant Force = F =SQRT (Fy2 + F12)

Resultant Force = F =SQRT (23.052 + 11.122)

Resultant Force = F =SQRT (531.30 + 123.65)

Resultant Force = F =SQRT (655)

Resultant Force = F = 25.60 KN

Hence, 2-M-16 Gr 8.8 bolt is safe enough to resist the Shear Force.

6. Conclusion:

All the materials used in the dome structure for all spans are structurally sufficient and meets its intended purpose.

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