﻿ 基于抗裂要求的楼面梁预应力筋数量及其影响因素探讨
 上海理工大学学报  2017, Vol. 39 Issue (4): 396-402 PDF

Discussion on the Number of Prestressed Tendons in Building Floor Beams and Its Influential Factors Based on Crack Resistance Requirement
XU Jianshe
School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: In the design of prestressed beams in building structures, the prediction of the number of prestreesed tendons is necessary.The tendon number meeting the demands of crack resistance was studied.The formulas for calculating the number of prestressed tendons under three crack resistance grades were listed.By introducing reasonable assumptions, the simplified calculation formulas for determining the tendon number at the mid-span and support point were provided.The various influential factors of the tendon number, e.g., the beam section shape, span of the beam, section width, crack resistance grade, slab thickness and position of prestressed tendons were discussed respectively.The relationship curves between the number and various influenctial factors were presented.The impact extent of various factors on the number was compared.A relatively accurate basis for estimating the number of prestressed tendons in the primary design phase was provided for structural designers.
Key words: prestressed beam     number of prestressed tendons     crack resistance

1 预应力筋数量的两种估算方法 1.1 平衡荷载法

 图 1 简支梁的平衡荷载 Fig. 1 Balanced load of simply supported beam

 (1)

 (2)

1.2 抗裂要求法

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)
2 预应力筋数量的影响因素

2.1 预应力筋数量计算的简化假定

a. 预应力筋为目前国内工程中最常用的1 860级ϕ15.24 mm钢绞线(fptk=1 860 N/mm2), 单根预应力筋的面积Ap1=140 mm2.

b. 预应力筋张拉控制应力σcon取0.7fptk, 即1 302 N/mm2.有效预应力σPe按0.8σcon估算(即预应力总损失按0.2σcon估算), 因而σpe=0.8×1 302=1 042 N/mm2.

c. 梁截面弯矩Mmax由经验系数法进行估算.梁的跨中弯矩Mmax1和端部弯矩Mmax2分别为

d. 梁的截面抵抗矩W和预应力筋偏心距e分两种截面考虑, 对于矩形截面(图 2(a))和T形截面(图 2(b)), 其We的取值可以统一表示为

 图 2 矩形和T截面特性 Fig. 2 Characteristic of rectangle and T shape section
 (11)
 (12)

2.2 预应力筋数量的简化计算公式

 (13)

 (14)

Ap1, σpe, Mmax的简化公式以及式(11) 和式(12) 带入式(13), 得

 (15)

2.3 预应力筋数量的影响因素

a. 荷载大小(gk+qk);

b. 截面位置(影响αβ的取值);

c. 梁跨度(l);

d. 抗裂等级;

e. 梁的截面特性(AIy1y2)

f. 预应力筋位置, 即预应力筋形心至梁截面边缘(顶面或底面)的距离(a1a2);

g. 混凝土的强度等级(对二、三级抗裂等级影响ftkσct1值).

3 预应力筋数量与各影响因素的关系

3.1 预应力筋数量与梁跨度的关系

 图 3 n与l的关系(一级, 矩形截面) Fig. 3 Relationship between n and l (grade 1, rectangle)

 图 4 n与l的关系(一级, T形截面) Fig. 4 Relationship between n and l (grade 1, T shape)

 图 5 n与l的关系(二级, 矩形截面) Fig. 5 Relationship between n and l (grade 2, rectangle)

 图 6 n与l的关系(二级, T形截面) Fig. 6 Relationship between n and l (grade 2, T shape)

 图 7 n与l的关系(三级, 矩形截面) Fig. 7 Relationship between n and l (grade 3, rectangle)

 图 8 n与l的关系(三级, T形截面) Fig. 8 Relationship between n and l (grade 3, T shape)
3.2 预应力筋数量与抗裂等级的关系

 图 9 各抗裂等级的n比较 Fig. 9 Comparison of value n for various crack resistance grades

3.3 预应力筋数量与截面形状的关系

 图 10 矩形和T形截面的n比较 Fig. 10 Comparison of n for rectangle and T shape sections

3.4 预应力筋数量与截面宽度的关系

 图 11 n与截面宽度的关系(一级) Fig. 11 Relationship between n and section width (grade 1)

 图 12 n与截面宽度的关系(二级) Fig. 12 Relationship between n and section width (grade 2)
3.5 预应力筋数量与T形截面翼缘板厚的关系

 图 13 n与hf的关系(一级) Fig. 13 Relationship between n and hf (grade 1)
3.6 预应力筋数量与预应力筋位置的关系

 图 14 n与预应力筋位置的关系 Fig. 14 Relationship between n and prestressed tendonpositions

4 结论

a. 预应力梁按抗裂计算所需的预应力筋根数的影响因素较多, 决不能单独根据跨度的大小直接预估.

b. 对预应力筋数量影响较大的因素有:荷载大小、梁跨度、抗裂等级、T形截面的翼缘板厚, 其中, 后者的影响效果最大.

c. 对预应力筋数量影响较小的因素有:梁的截面宽度、梁的截面形状、预应力筋在截面的位置.增加梁截面宽度或改变预应力筋在梁高度方向的位置并不能有效减少预应力筋的数量.

d. 增加板厚(即增加T形截面的翼缘板厚度), 在三级抗裂等级的情况下可以显著减少预应力筋数量.

e. 在方案及初步设计阶段, 采用本文给出的估算式(15) 可以方便地预估预应力筋抗裂计算所需的预应力筋数量.

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