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DESIGN OF BEAM-COLUMN WITH A RECTANGULAR SECTION SUBJECTED TO

AXIAL AND MOMENT LOADS ABOUT THE X-AXIS USING ACI 318-11

FACTORED LOAD DEMAND

P.u 5300 kN * :

Factored Axial Load Demand

ONLY ENTRIES WITH A YELLOW BACKGROUND CAN BE MODIFIED

M.u 340 kN * m * :

Factored Moment Demand

MATERIAL AND GEOMETRIC PROPERTIES

h.x 90 cm * :

Section Depth

b.x 20 cm * :

Section Width

f'.c 45 MPa * :

Concrete Strength

f.y 400 MPa * :

Steel Strength

E.s 2105^* MPa * :

Modulus of Elasticity of Steel (ACI 8.5.2)

β f'.c 28 MPa * ≤ 0.85 0.85 f'.c 28 MPa * - 7 MPa * / .05 * (- 0.65 21 mat max if : 0.7286

Factor for Equivalent Rectangular Stress Block (ACI 10.2.7.3)

AREA AND LOCATION OF STEEL

d' 20 mm * :

Ds.Rebar 13 mm * :

S.Ver 50 mm * :

D.Rebar 22 mm * :

COL.rebar 2 :

N.ver h.x 2 d' * - 2 Ds.Rebar * - (S.Ver / 2 / (0 round : 8

i 1 : i N.ver ≤ i i 1 + : j 1 : j COL.rebar ≤ j j 1 + : i 1 > (j 1 > (& (i N.ver < (j COL.rebar < (& (& n.b i j el 0 : n.b i j el 1 : if for for

co d' Ds.Rebar + D.Rebar 2 / + : 0.044 m *

j 1 : j n.b rows ≤ j j 1 + : k 0 : i 1 : i COL.rebar ≤ i i 1 + : k n.b j i el k + : for n.sl j el k : 31 line for

d'.x Δ h.x 2 co * - N.ver 1 - / : d 1 el co : i 2 n.b rows range d i el Δ i * d 1 el + : 11 line for d 41 line :

A.sb π D.Rebar 2^* 4 / :

A.s_x A.sb n.sl * :

A.s_tot A.s_x i el i 1 A.s_x rows sum : 0.0061 m 2^*

A.s_x mm 2^760.2654 760.2654 760.2654 760.2654 760.2654 760.2654 760.2654 760.2654 81 mat

d'.x mm 4427639250862474085697281 mat

Steel Area

Distance of the Centroid of Steel from the Top of the Section

A.s_tot A.s_x sum : mm 2^6082.1234

Total Steel Area

A.s_chk A.s_tot 0.01 h.x * b.x * ≤ NG, Requires More Steel Area A.s_tot 0.08 h.x * b.x * ≥ NG, Reduce Steel Area OK if if :

A.s_chk OK

Steel Limit for Columns (ACI 318-11 10.9.1)

STEEL STRAIN

n d ε.x .003 n / (n d - (* :

STEEL STRESS

n d f.s n d ε.x f.y E.s / ≥ f.y n d ε.x f.y - E.s / ≤ f.y - E.s n d ε.x * if if :

STEEL FORCE

n d A.s F.s n d f.s A.s * :

CONCRETE FORCE

n C.x 0.85 f'.c * β * n b.x * n d'.x i el < 0 A.s_x i el if i 1 d'.x rows sum - (* :

AXIAL LOAD AND MOMENT CAPACITY

n P.nx n C.x n d'.x i el A.s_x i el F.s (i 1 A.s_x rows sum + :

Axial Capacity based on Excentricity

n M.nx n C.x h.x 2 / β n * 2 / - (* n d'.x i el A.s_x i el F.s d'.x i el h.x 2 / < h.x 2 / d'.x i el - d'.x i el h.x 2 / - (1 - (* if * (i 1 A.s_x rows sum + :

Moment Capacity based on Excentricity

φ.a 0.65 :

Resistance Factor for Tied Columns (ACI 318-11 9.3.2.2)

Reduction Factor for Maximum Axial Load for Tied Columns ACI 318-11 10.3.6.2)

α 0.8 :

αφP.n_max α φ.a * 0.85 f'.c * b.x h.x * A.s_tot - (* A.s_tot f.y * + (* : kN 4724.31

Maximum Axial Load (ACI 318-11 10.3.6.2)

P.0 kN :

M.0 kN m * :

ds 0.005 m * :

Generate Data for Nominal Strength Plot i 1 h.x 1.4 * ds / trunc range P i 1 el i ds * M.nx M.0 / eval : P i 2 el i ds * P.nx P.0 / eval : 21 line for Reducing Matrix of nonuseful entries i 1 P rows range P i 1 el 0 > (P i 2 el 0 > (& sub1 i 1 + (: continue if for i 1 P rows range P i 2 el 0 < sub2 i 1 - (: break if for P_M.n P sub2 sub1 12 submatrix : Generate Data for ACI Design Strength Plot i 1 P_M.n rows range φP_M.n i 1 el φ.a P_M.n * i 1 el eval : φP_M.n i 2 el φ.a P_M.n * i 2 el αφP.n_max P.0 / 21 mat min eval : 21 line for Generate Lines for Load Demand Pu_Mu 0 P.u M.u P.u M.u 032 mat 1 M.0 / 001 P.0 / 22 mat * : 101 line

φP_M.n P_M.n Pu_Mu 3 1 sys

Find n to match Pnx = pu

P.u kN 5300

n P.nx P.u ≡ n solve #

80 cm * P.nx kN 5338.3268

find Mnx(n)

n M.nx #

80 cm * M.nx kN m * 902.9569

How can I find a n value that matches Pnx = pu