OPTION 1:
L ≔ 2.2 m
Span
b ≔ 4.0 m
Plate width
w ≔ 50 mm
Plate thickness
kN
γs ≔ 77 ――
m3
Unit weight of steel
Fy ≔ 300 MPa
Yield strength
E ≔ 200 GPa
Modulus of elasticity
kN
wD ≔ γs ⋅ w ⋅ b = 15.4 ――
m
Weight of plate
PL ≔ 175 kN
Live load for flexural design
DLA ≔ 0.4
Dynamic load allowance
wD ⋅ L 2
MD ≔ ―――
= 9.32 kN ⋅ m
8
((1 + DLA)) ⋅ PL ⋅ L
= 135 kN ⋅ m
ML ≔ ――――――
4
Dead load moment
Live load moment
M ≔ MD + ML = 144 kN ⋅ m
SLS Moment
Mf ≔ 1.1 MD + 1.7 ML = 239 kN ⋅ m
ULS Moment
b ⋅ w3 ⎛
I ≔ ――= ⎝41.667 ⋅ 10 6 ⎞⎠ mm 4
12
b ⋅ w2 ⎛
S ≔ ――= ⎝2 ⋅ 10 6 ⎞⎠ mm 3
6
Mr ≔ 0.95 S ⋅ Fy = 475 kN ⋅ m
Vr ≔ 0.577 Fy ⋅ b ⋅ w = 34620 kN
Moment of inertia
Section modulus
Mf
= 0.504 Ok ULS check
――
Mr
Shear resistance. Do not control
4
5 wD ⋅ L
δD ≔ ――
⋅ ―――
= 0.564 mm
384
E⋅I
Dead load deflection
((1 + DLA)) ⋅ PL ⋅ L 3
δL ≔ ――――――= 6.5 mm
48 E ⋅ I
Live load deflection
L
δT ≔ δD + δL = 7.086 mm < ――
= 7.333 mm Ok
300
OPTION 2:
L ≔ 2.5 m
Span
b ≔ 1.6 m
Plate width
w ≔ 60 mm
Plate thickness
kN
γs ≔ 77 ――
m3
Unit weight of steel
Fy ≔ 300 MPa
Yield strength
E ≔ 200 GPa
Modulus of elasticity
kN
wD ≔ γs ⋅ w ⋅ b = 7.392 ――
m
Weight of plate
PL ≔ 87.5 kN
Live load for flexural design
DLA ≔ 0.4
Dynamic load allowance
wD ⋅ L 2
MD ≔ ―――
= 5.78 kN ⋅ m
8
((1 + DLA)) ⋅ PL ⋅ L
= 77 kN ⋅ m
ML ≔ ――――――
4
Dead load moment
Live load moment
M ≔ MD + ML = 82 kN ⋅ m
SLS Moment
Mf ≔ 1.1 MD + 1.7 ML = 137 kN ⋅ m
ULS Moment
b ⋅ w3 ⎛
I ≔ ――= ⎝28.8 ⋅ 10 6 ⎞⎠ mm 4
12
b ⋅ w2 ⎛
S ≔ ――= ⎝960 ⋅ 10 3 ⎞⎠ mm 3
6
Mr ≔ 0.95 S ⋅ Fy = 274 kN ⋅ m
Vr ≔ 0.577 Fy ⋅ b ⋅ w = 16618 kN
Moment of inertia
Section modulus
Mf
= 0.499 Ok ULS check
――
Mr
Shear resistance. Do not control.
4
5 wD ⋅ L
δD ≔ ――
⋅ ―――
= 0.65 mm
384
E⋅I
Dead load deflection
((1 + DLA)) ⋅ PL ⋅ L 3
δL ≔ ――――――= 6.92 mm
48 E ⋅ I
Live load deflection
L
δT ≔ δD + δL = 7.58 mm < ――
= 8.33 mm Ok
300
SLS check