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bl = 1000 mm tl = 18 mm
Al = tl * bl = 18x1000 = 18000 mm2
Il = [ bl * ( tl ^3) ]/ 12 = 486000 mm4
Sl = Il / ( tl / 2)= 54000 mm3
Ƥmax = p = 58.5 kN/m2 = 0.0585 N/mm2
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| body | --uriencoded--$$ \normalsize L_%7Bbk%7D = min \left ( 3.16 \sqrt%7B \frac%7Bf_%7Bel%7D S_l%7D%7Bpb_l G K%7D%7D \, \, \, \, , \quad 0.835 \sqrt [3] %7B \frac%7BE_l I_l%7D%7Bpb_l%7D%7D \, \, \, \, , \quad \frac%7Bf_%7Bkl%7D A_l%7D%7B0.9 pb_l G K%7D \right ) \qquad \qquad \qquad \qquad \qquad \qquad (2) \\ L_%7Bbk%7D = min \left ( 3.16 \sqrt%7B \frac%7B30 \times 54000%7D%7B0.0585 \times 1000 \times 2.0%7D%7D \, \, \, \, , \quad 0.835 \sqrt [3] %7B \frac%7B10000 \times 486000%7D%7B0.0585 \times 1000%7D%7D \, \, \, \, , \quad \frac%7B3 \times 18000%7D%7B0.9 \times 0.0585 \times 1000 \times 2.0%7D \right ) = min(371.8 \, , \, 364.3 \, , \, 512.8) \\ L_%7Bbk%7D = 364.3 \, mm = 36.43 \, cm $$ |
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Secondary beam interval, Lik
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Lbk = 364.3mm
Abk = 9640 mm2
Ibk = 45701333.333 mm4
Sbk = 457013.333 mm3
febk = 30 MPa
febk = 3.0 MPa
Ebk = 14000 MPa
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| body | --uriencoded--$$ \normalsize L_%7Bik%7D = min \left ( 3.16 \sqrt%7B \frac%7Bf_%7Bebk%7D S_%7Bbk%7D%7D%7Bp L _%7Bbk%7D G K%7D%7D \, \, \, \, , \quad 0.835 \sqrt [3] %7B \frac%7BE_%7Bbk%7D I_%7Bbk%7D%7D%7Bp L _%7Bbk%7D%7D%7D \, \, \, \, , \quad \frac%7Bf_%7Bkbk%7D A_%7Bbk%7D%7D%7B0.9 p L _%7Bbk%7D G K%7D \right ) \qquad \qquad \qquad \qquad \qquad \qquad (3) \\ L_%7Bik%7D = min \left ( 3.16 \sqrt%7B \frac%7B30 \times 457013.33%7D%7B0.0585 \times 364.3 \times 2.0%7D%7D \, \, \, \, , \quad 0.835 \sqrt [3] %7B \frac%7B14000 \times 45701333.33%7D%7B0.0585 \times 364.3%7D%7D \, \, \, \, , \quad \frac%7B3 \times 9640%7D%7B0.9 \times 0.0585 \times 364.3 \times 2.0%7D \right ) = min(1792.1 \, , \, 2595.1 \, , \, 753.8) \\ L_%7Bik%7D = 753.8 \, mm = 75.38 \, cm $$ |
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Rod Interval, Lb
2xUPN 80 was chosen as the secondary beam section.
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Lik = 753.8 mm
Aik = 2185.3 mm2
Iik= 2.0921x10 6 mm4
Sik = 52303 mm3
feik = 30 MPa
feik = 3.0 MPa
Eik = 14000 MPa
Rod diameter Φ = 17 mm
Rod tensile capacity, Nd,b
Nd,b = [ ( π* 2 ) / 4 fyb = [ ( π*172 ) / 4 ] 235 = 53340.32 N = 53.34 kN
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| body | --uriencoded--$$ \normalsize L_%7Bb%7D = min \left ( 3.16 \sqrt%7B \frac%7Bf_%7Beik%7D S_%7Bik%7D%7D%7Bp L _%7Bik%7D G K%7D%7D \, \, \, \, , \quad 0.835 \sqrt [3] %7B \frac%7BE_%7Bik%7D I_%7Bik%7D%7D%7Bp L _%7Bik%7D%7D%7D \, \, \, \, , \quad \frac%7Bf_%7Bkik%7D A_%7Bik%7D%7D%7B0.9 p L _%7Bik%7D G K%7D \, \, \, \, , \quad \frac%7BN_d%7D%7B1.1 p L _%7Bik%7D G K%7D \right ) \qquad \qquad \qquad \, \, (4) \\ L_%7Bb%7D = min \left ( 3.16 \sqrt%7B \frac%7B235 \times 52303%7D%7B0.0585 \times 753.8 \times 2.0%7D%7D \, \, \, \, , \quad 0.835 \sqrt [3] %7B \frac%7B200000 \times 2.0921*10%5e6%7D%7B0.0585 \times 753.8%7D%7D \, \, \, \, , \quad \frac%7B141 \times 2185.3%7D%7B0.9 \times 0.0585 \times 753.8 \times 2.0%7D \, \, \, \, , \quad \frac%7B53340.32%7D%7B1.1 \times 0.0585 \times 753.8 \times 2.0%7D \right ) = min(1179.7 \, , \, 1767.7 \, , \, 3884.9 \, , \, 549.8) \\ L_%7Bb%7D = 549.8 \, mm = 54.98 \, cm $$ |
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Prop Control
Axial load capacity of the support Nd = 9.7 kN
c = 1.2
q = 0.5 kN/m 2
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