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Plate Check

The document presents a design check for a 10 mm thick plate subjected to live load and acceleration, detailing material and physical properties, design loads, and checks for bending, shear, and deflection. All checks indicate that the plate is adequate, with unity check ratios for bending strength, shear strength, and deflection being 0.308, 0.006, and 0.924 respectively, all below 1. The conclusion confirms that the 10 mm plate meets the necessary structural requirements.

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Chinnaraja Gandhi
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59 views3 pages

Plate Check

The document presents a design check for a 10 mm thick plate subjected to live load and acceleration, detailing material and physical properties, design loads, and checks for bending, shear, and deflection. All checks indicate that the plate is adequate, with unity check ratios for bending strength, shear strength, and deflection being 0.308, 0.006, and 0.924 respectively, all below 1. The conclusion confirms that the 10 mm plate meets the necessary structural requirements.

Uploaded by

Chinnaraja Gandhi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLS, PDF, TXT or read online on Scribd
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PLATE DESIGN - UDL : ROARK'S CHECK

MODULE : REFERENCES

PLATE ID :

REF. DRG :

Support at the edges of plate: = FIXED


Load Case: Live Load + Max.Acceleration (operating)

1.0 Material Properties:


Yield strength, Fy = 245 N/mm²
Modulus of Elasticity, E = 200000 N/mm²
Density of steel r = 7850 kg/m3
= 7850*9.81/1000
= 77.01 kN/m3
2.0 Physical Properties:
Length of the plate, a = 3.50 m
Width of the plate, b = 2.00 m
Assumed thickness of plate, t = 10.00 mm
Contingency factor, C.F = 1.15
Acceleration coeff in vertical direction, accln = 1.00

3.0 Design Loads:


Live Load, LL = 2.50 KN/mm²

Self weight of plate with Contingency Factor, Sw = t∗ρ∗C . F


= (10/1000)*77.01*1.15
= 0.89 KN/m²

Udl with acceleration due to self weight+LL, q = ( LL∗acc ln )+( sw∗acc ln)
= (2.5*1)+(0.89*1)
= 3.39 KN/m²

4.0 Check for Stresses:

4.1 Check for Bending:

a/b 1 1.2 1.4 1.6 1.8 2 ∞ From [R1] Table 11.4


b1 0.3078 0.3834 0.4356 0.4680 0.4872 0.4974 0.5000 case 8(a)
b2 0.1386 0.1794 0.2094 0.2286 0.2406 0.2472 0.2500
a 0.0138 0.0188 0.0226 0.0251 0.0267 0.0277 0.0284

The value of a/b = 3.5/2


= 1.75

The value of a/b lies between a/b 2 ∞


b1 0.4974 0.5000
b2 0.2472 0.2500
a 0.0277 0.0284
Interpolated value of b1 = 0.5000 REFERENCES
Interpolated value of α = 0.0284
2
Maximum bending moment at centre of long edge (b1 =1m) = β 1∗q∗b2 b 1∗t
2
∗
t 6

= 0.5 * 3.39 * 2² 1*(10/1000)²


*
(10/1000)² 6
Total Maximum bending moment at centre of long edge, M = 1.130 kNm/m

2
b∗t
Elastic Section Modulus ,S =
6
= 1000*10²
6
= 16666.67 mm3
b∗t 2 ###
Plastic Section Modulus ,Z =
4
= 1000*10²
4
= 25000.00 mm3

Mn = Mp = Fy*Zx ≤ 1.6*My R2, Eqn F6-1


Ωb = 1.67

1.6*My = 1.6*Fy*S

= 1.6*245*16666.67

= 6533334.64 N-mm

= 6.53 kN-m

Mp = Fy*Zx = 245*25000

= 6125000.00 N-mm

= 6.13 kN-m

Allowable moment Mal = (1/Ωb)*Min(Mp,1.6My)

= (1/1.67)*MIN(6.125,6.53)

= 3.67 kN-m

Unity check ratio = ( M / Mal )


= 1.13/ 3.67
= 0.308 <1, OK
4.2 Check for Shear:
Maximum shear force,R = 0 . 5∗q∗a
= 0.5 * 3.39 * 3.5
= 5.93 kN/m
Aw = b1*t
= 1000*10
= 10000.00
Ωv = 1.50 R2, Eqn G2-1
Cv = 1.00
Allowable shear strength, Rall = (1/Ωv)*(0.6*Fy*Aw*Cv) R2, Eqn G2-2
= (1/1.5)*(0.6*245*10000*1)/(1000)
= 980.00 kN/m

Unity check ratio = ( R / Rall)


= (5.93/ 980)
= 0.006
= 0.006 <1, OK
5.0 Check for Deflection:
Maximum deflection due to self weight,∂ = α∗q∗b 4
= E∗t 3
= ((0.0284* 3.39* 2^4)/(200000* (10/1000)^3))
= 7.70 mm
REFERENCES
Allowable deflection,∆ = b
240
= (2*1000)/240
= 8.33 mm
= Actual < Allowable,O.K

Unity check ratio = ∂


Δ
= 7.7/8.33
= 0.924 <1, OK

6.0 Summary:

Section Description UC Ratio Status

4.1 Bending Strenth 0.308 OK

4.2 Shear Strength 0.006 OK

5.0 Deflection 0.924 OK

7.0 Conclusion :

10 mm PLATE IS ADEQUATE

8.0 References :

[R1] - "Roark's Formulas for Stress & Strain" by W.C.Young (7th edition)
[R2] - Structural steel specification (ASD) - AISC 13th Edition.

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