一、设计示意图
二、基本资料
1车辆排队长度.设计规范:
《混凝土结构设计规范》(GB50010—2002)
2.几何参数:
楼梯类型:梁式C型楼梯( / ̄ )
约束条件:两端简支
楼梯上部平台水平段长度: L2 = 500 mm
梯段净跨: Ln = L1 + L2 = 3000 + 500 = 3500 mm
楼梯高度: H = 1650 mm 楼梯宽度: W = 1200 mm
踏步高度: h = 150 mm 踏步宽度: b = 300 mm
楼梯级数: n = 11(级) 梯段板厚: C = 100 mm
平台板厚: C1 = 80 mm
面层厚度: C2 = 30 mm
下部平台梯梁宽度: b2 = 200 mm
楼梯梁宽度: b3 = 200 mm
楼梯梁高度: h3 = 300 mm
3.荷载参数:
楼梯混凝土容重: b = 25.00 kN/m3
楼梯面层容重: c1 = 25.00 kN/m3
楼梯顶棚抹灰容重: c2 = 25.00 kN/m3
楼梯栏杆自重: qf = 0.50 kN/m
楼梯设计可变荷载标准值: q = 2.50 kN/m2
可变荷载组合值系数: c = 0.70
可变荷载准永久值系数: q = 0.50
4.材料参数:
混凝土强度等级: C25
混凝土抗压强度设计值: fc = 11.90 N/mm2
混凝土抗拉强度标准值: ftk = 1.78 N/mm2
混凝土抗拉强度设计值: ft = 1.27 N/mm2
混凝土弹性模量: Ec = 2.80 104 N/mm2
主筋强度等级: HPB235(Q235) fy = 210.00 N/mm2
主筋弹性模量: Es = 210000 N/mm2
其他钢筋强度等级: HPB235(Q235) fyv = 210.00 N/mm2
其他钢筋弹性模量: Es = 210000 N/mm2
受拉纵筋合力点到梯梁底边的距离: as = 15 mm
三、荷载计算过程
1.楼梯几何参数:
梯段板与水平方向夹角余弦值: cos = = = 0.89
梯梁的计算跨度: L0 = Min{Ln + (b1 + b2) / 2,1.05Ln} = Min{3500 + (200 +
200) / 2,1.05 3500} = Min{3700,3675} = 3675 mm
梯段板的净宽度: B = W - 2b3 = 1200 - 2 200 = 800 mm
梯段板的计算跨度: B 0 = Min{B + b3,1.05B} = {800 + 200,1.05 800}
= Min{1000,840} = 840 mm通用机关零件
梯段板的平均厚度: T = (h + C / cos 2) / 2 = (150 + 100 / 0.89 2) / 2
= 187 mm
2.荷载设计值
2.1 均布恒载标准值:
2.1.1 L1段楼板自重
gk1' = b T / 1000 = 25.00 187 / 1000 = 4.67 kN/m2
gk1 = gk1' L1 / Ln = 4.67 3000 / 3500 = 4.00 kN/m2
2.1.2 L2段梯板自重:
gk2' = b t1 / 1000 = 25.00 80 / 1000 = 2.00 kN/m2
gk2 = gk2' L2 / Ln = 2.00 500 / 3500 = 0.29 kN/m2
2.1.3 L1段梯板面层自重:
gk3' = c1 C2 (H + L1) / L1 / 1000 = 25.00 30 (1650 + 3000) / 3000 / 1000
= 1.16 kN/m2
gk3 = gk3' L1 / Ln = 1.16 3000 / 3500 = 1.00 kN/m2
2.1.4 L2段梯板面层自重:
gk4' = c1 C2 / 1000 = 25.00 30 / 1000 = 0.75 kN/m2
gk4 = gk4' L2 / Ln = 0.75 500 / 3500 = 0.11 kN/m2
梯段斜板恒荷载标准值: gkx = gk1' + gk3' = 4.67 + 1.16 = 5.83 kN/m2
梯板折算永久荷载标准值: gkb = gk1 + gk2 + gk3 + android模拟器gk4 = 4.00 + 0.29 + 1.00 + 0.11
= 5.39 kN/m2
考虑到面层重量等对梯梁的作用,梯梁自重放大系数b取1.1
梯梁自重的标准值: gkL = b b b3 h3 [Ln + L1 (1 / cos - 1)] / Ln /
1000000 = 1.10 25.00 200 300 [3500 + 3000 (1 / 0.89 - 1)] / 3500 /
1000000 = 1.82 kN/m
梯梁上永久荷载标准值: gk = gkb B / 2000 + gkL + qf = 5.39 800 / 2000 + 1.82
+ 0.50 = 4.47 kN/m
2.2 均布荷载设计值:
由活荷载控制的梯段斜板荷载设计值: pxL = 1.2gkx + 1.4q = 1.2 5.83 + 1.4 2.50
= 10.50 kN/m2
由恒荷载控制的梯段斜板荷载设计值: pxD = 1.35gkx + 1.4cq = 1.2 5.83 + 1.4
2.50 0.70 = 10.32 kN/m2
最不利的梯段斜板荷载设计值: px = Max{pxL,pxD} = Max{10.50,10.32}
= 10.50 kN/m2
由活荷载控制的梯梁荷载设计值: pL = 1.2gk + 1.4 q W / 2 / 1000 = 1.2 4.47 +
1.4 0.70 1200 / 2 / 1000 = 7.47 kN/m
由恒荷载控制的梯梁荷载设计值: pD = 1.35gk + 1.4 c q W / 2 / 1000
= 1.2 5.83 + 1.4 2.50 0.70 1200 / 2 / 1000 = 7.51 kN/m
最不利的梯梁荷载设计值: p = Max{pL,pD} = Max{7.47,7.51} = 7.51 kN/m
四、正截面承载能力计算
1.梯段斜板计算:
梯段斜板按简支计算,其最大弯矩在跨中: Mmax = 台球杆架pxB02 10-6 = 10.50
8402 1000 10-9 = 0.31 kN·m
1) 相对界限受压区高度b
cu = 0.0033 - (fcu,k - 50)10-5 = 0.0033 - (25 - 50)10-5 = 0.0036 >0.0033
取cu = 0.0033
按规范公式(7.1.4-1)
b = = = 0.61
2) 受压区高度x
按规范公式(7.2.1-1),A's = 0,A'p = 0
M = 1fcbx
x = h0 - = 162- = 0.16mm
< bh0 = 0.61162 = 99.46mm, 按计算不需要配置受压钢筋
3) 受拉钢筋截面积As
按规范公式(7.2.1-2)
1fcbx = fyAs
得 As = = = 9.08mm2
4) 验算配筋率
= = = 0.00% < max = 2.50% 不超筋
按最小配筋率要求配筋, As = minbh = 509mm2
实配实际配置受拉钢筋为: A10@150, As = 523.60mm2
2.梯梁配筋计算:
跨中最大弯矩,Mmax = pL02 地沟油检测方法 10-6 = 7.51 36752 10-6
= 12.68 kN·m
1) 相对界限受压区高度b
cu = 0.0033 - (fcu,k - 50)10-5 = 0.0033 - (25 - 50)10-5 = 0.0036 >0.0033
取cu = 0.0033
按规范公式(7.1.4-1)
b = = = 0.61
2) 受压区高度x
按规范公式(7.2.1-1),A's = 0,A'p = 0
M = 1fcbx
x = h0 - = 285- = 19.35mm
< bh0 = 0.61285 = 174.98mm, 按计算不需要配置受压钢筋
3) 受拉钢筋截面积As
按规范公式(7.2.1-2)
1fcbx = fyAs
得 As = = = 219.27mm2
4) 验算配筋率
= = = 0.37% < max = 2.50% 不超筋
满足最小配筋率要求
实配受拉钢筋(底部): 2A12, As = 226.19mm2
五、斜截面承载能力计算
1.箍筋
Vmax = 0.5pLn = 0.5 7.51 3500 / 1000 = 13.80 kN
1) 复核截面条件
按规范公式(7.5.1-1)
0.25cfcbh0 = 0.251.0011.90200(300 - 15.00) 10-3 = 169.58 kN
V = 13.80kN < 0.25cfcbh0 = 169.58kN, 截面尺寸满足要求
2) 验算构造配筋条件
按规范公式(7.5.7-1)
0.7ftbh0 = 0.7 不锈钢液压管接头 1.27 200 285 / 1000 = 50.67 kN > V = 13.80kN
按构造配置箍筋
实际配置双肢箍筋 A6@200
六、跨中挠度验算
1.荷载效应的标准值组合:
pk = gk + 0.5qW / 1000 = 4.47 + 0.5 2.50 1200 / 1000 = 5.97 kN/m
Mk = pkL02 10-6 = 5.97 36752 10-6 = 10.09 kN·m
2.荷载效应的准永久值组合:
pq = gq + 0.5qqW / 1000 = 4.47 + 0.5 0.50 2.50 1200 / 1000 = 5.22 kN·m