题目
某矩形截面梁(二级安全级别、一类环境条件)，截面尺寸为b times h = 200mm times 500mm。混凝土为C20，钢筋为HRB335级。持久设计状况下，承受弯矩设计值M = 190kN cdot m。已配有2 Phi 25(A_(s)^prime = 982mm^2)纵向受压钢筋，试计算受拉钢筋面积。（f_(c) = 9.6N/mm^2，f_(y) = 300N/mm^2，a = 60mm，a^prime = 35mm，rho_(min) = 0.2%，xi_(b) = 0.55，xi = 1 - sqrt(1 - 2alpha_(i))，K取1.2，alpha_(s) = (KM - f_(y) cdot A_(s)^prime (h_(0) - a))/(f_(c) b h_{0)^2}）【单选题】A_(s)为多少？()A. 1900mm^2B. 1973mm^2C. 1980mm^2D. 1561mm^2
某矩形截面梁(二级安全级别、一类环境条件)，截面尺寸为$b \times h = 200mm \times 500mm$。混凝土为C20，钢筋为HRB335级。持久设计状况下，承受弯矩设计值$M = 190kN \cdot m$。已配有$2 \Phi 25$($A_{s}^{\prime} = 982mm^{2}$)纵向受压钢筋，试计算受拉钢筋面积。（$f_{c} = 9.6N/mm^{2}$，$f_{y} = 300N/mm^{2}$，$a = 60mm$，$a^{\prime} = 35mm$，$\rho_{min} = 0.2\%$，$\xi_{b} = 0.55$，$\xi = 1 - \sqrt{1 - 2\alpha_{i}}$，K取1.2，$\alpha_{s} = \frac{KM - f_{y} \cdot A_{s}^{\prime} (h_{0} - a)}{f_{c} b h_{0}^{2}}$）
【单选题】
$A_{s}$为多少？()
A. $1900mm^{2}$
B. $1973mm^{2}$
C. $1980mm^{2}$
D. $1561mm^{2}$
题目解答
答案
根据题目条件，$ h_0 = 440 \, \text{mm} $，$ K M = 228 \times 10^6 \, \text{N·mm} $，$ f_y' A_s' (h_0 - a') = 119,313,000 \, \text{N·mm} $。
\[
\alpha_s = \frac{228 \times 10^6 - 119,313,000}{1.0 \times 9.6 \times 200 \times 440^2} = \frac{108,687,000}{371,712,000} \approx 0.2924
\]
\[
\xi = 1 - \sqrt{1 - 2 \times 0.2924} \approx 0.3556 < \xi_b = 0.55
\]
\[
x = \xi h_0 = 0.3556 \times 440 \approx 156.46 \, \text{mm}
\]
\[
A_s = \frac{\alpha_1 f_c b x + f_y' A_s'}{f_y} = \frac{1.0 \times 9.6 \times 200 \times 156.46 + 300 \times 982}{300} \approx 1,980 \, \text{mm}^2
\]
最终结果为 $ A_s = 1,980 \, \text{mm}^2 $。
答案：C. 1980 mm²