螺旋楼梯计算书

螺旋楼梯计算书1、几何参数

平面示意图b’=1.45m b=1.25m r=1.50mμ=25级高度h=3.84m

β=300°=300π

180

=5.236rad

楼梯内侧辐射半径r1=r−b’

2=1.5−1.45

2

=0.775m

楼梯外侧辐射半径r2=r+b’

2=1.5+1.45

2

=2.225m

每一个踏步水平旋转角ω=β

μ=300°

25

=12°=12π

180

=0.2094rad

每个踏步高度a=ℎ

μ=3.840

25

=0.1536m

楼梯宽度中心线处倾斜角φ=arctanℎ

βr =arctan 3.84

1.5x5.236

=26°03′

cosφ=0.8984 sinφ=0.4392

楼梯计算轴线长度s=βr

cosφ=1.5x5.236

0.8984

=8.74m

2、设计荷载

楼梯板厚度t=s

30=8.74

30

=0.29m 取t=0.3m

设计荷载的作用半径R≈r+b’2

12r =1.5+ 1.452

12x1.5

=1.62m

m=R

r =1.62

1.5

=1.08

可变荷载q=γ

QQ r b′

m

=1.4x4x1.45

1.08

=7.52

永久荷载g=γ

G(G+G′）’

Rω

踏步示意图

e=t

cosφ=0.300

cos26°03′

=0.334m

G=27x a+2e

2x[ω(r22−r12)]

2

=27x 0.1536+2x0.334

2

×

[0.2094x(2.2252−0.7752）]

2

=4.68KN

1m2水平投影面上30mm厚水磨石及底板20mm石灰粉刷的永久荷载标准值：

G′=22x0.03x a+rω

rω+17×0.02×rω×1

cosφ

=22x0.03x 0.1536+1.62x0.2094

1.62x0.2094

+0.34×1.62×0.2094×

1

cos26°03′

=1.09KN/m2

g=1.2x(4.6778+1.09)

1.62x0.2094

=20.41KN/m

p=g+q=20.41+7.51=27.92KN/m

3、内力计算及配筋

上半段内力正方向示意图a．跨中截面M r= -42.91KN·m V r=−100.74KN 截面尺寸验算：

0.25f c t b0=0.25x14.3x300x1220=1308.45KN>V r

单筋矩形截面抗弯计算

X=t0− t02−2M r

αf c b =270−2702−2x42.91x106

14.3x1250

=9.04mm

As=Xf c b

f y

=449mm2

b．上支座截面M r=0M n=−68.34KN·m

T=−31.84KN·m V r=87.24KN V n=−82.98KN N=-98.29KN（拉力）截面尺寸验算：

W t=t2

6

3b−t=

3002

6

3x1250−300=5.175x107mm3

V n

bt0

2

+

V r

tb0

+

T

0.8W t

2

=−82.98x1032

+

87.24x103

+

31.84x106

7

2 =1.037N/mm2<0.25f c=3.575 N/mm2

∴截面尺寸满足要求

1.037N/mm2>0.7f t=1.001 N/mm2

∴需要根据计算确定剪扭箍筋面积

（1）计算V r，T的剪扭计算面积

W t=5.175x107mm3

βt=

1.5

1+0.5W t V r

T t b0

=

1.5

1+0.5x5.175x107x87.24x103

31.84x106x300x1220

=1.256>1 取1 V r≤ 1.5−βt0.7f t t b0+f y v

A sv

b0

= 1.5−10.7x1.43x300x1220+360x

A sv

s

x1220

A sv

=

87.24x103−183183

<0

∴构造配抗剪箍筋

承受弯剪扭最小配箍率ρsvmin=0.28f t

f yv =0.28x1.43

360

=0.111%

A svmin=ρsvmin b s=208mm2

T≤βt0.35f t W t+1.2 ξf y v A st1A cor

s

ξ=f y A stL S

f yv A st1u cor

取1.2