mathcad - steel area design rectangular section bs8110-1
TRANSCRIPT
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BS8110-1 REINFORCED RECTANGULAR SECTION
Given:
Mu 6.0 kN m moment
b 1000 mm width
d 144 mm effective depth
d' 56 mm depth of the compression steel from the comprssion face
fcu 40 MPa compressive strength
fy 460 MPa yield strength
Solution:
Mmax 0.156 fcu b d2 129.393 kN m BS 3.4.4.4
checkM "provide compressive reinforcement" Mu Mmaxif"Single reinforced" otherwise
checkM "Single reinforced"
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Mu < Mmax, no compression reinforcement is required
KconcMu
fcu b d27.234 10 3
z d 0.5 0.25Kconc
0.9
142.833 mm BS 3.4.4.4
checkz "z > 0.95d"zd
0.95if
"OK" otherwise
"z > 0.95d"
zd
0.992
xd z0.45
2.593 mm
checkx "x > 0.5d" xd2
if
"OK" otherwise
"OK"
d2
72 mm
AsMu
0.87 fy z 104.965 mm2 BS 3.4.4.4
100Asb d 0.073
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Asminper 0.13 fy 460 MPa=if0.24 fy 250 MPa=if"fy is 250 MPa or 460MPa" otherwise
0.13 BS Table 3.25
Asminper b d100
187.2 mm2
Asgovern max AsAsminper b d
100
187.2 mm2
Mu > Mmax, area of compression reinforcment As' is required
f's 700 MPa 1 2 d'd
155.556 MPa BS 3.4.4.4
checkf's "f`s > 0.95fy" f's 0.95 fyif"OK" otherwise
"OK"
0.95 fy 437 MPa
As'Mmax Mu
f's 0.67fcu1.5
d d'( )
10183.749 mm2 BS 3.4.4.4
0.2 b d100
288 mm2 BS Table 3.25100
As'b d 7.072
As'govern max As'0.2 b d
100
10183.749 mm2
z' d 0.5 0.250.156
0.9
0.112 m BS 3.4.4.4
AsMmax
0.95 fy zMu Mmax
0.95 fy d d'( ) 1135.671 mm2 BS 3.4.4.4
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As is to be placed at the bottom of the beam and As' at the top forpositive bending and vice versa for negative bending