弹体侵彻钢筋混凝土遮弹层的阻力方程

王武; 杨军; 王安宝; 李胜杰

doi:10.11883/bzycj-2024-0217

弹体侵彻钢筋混凝土遮弹层的阻力方程

doi: 10.11883/bzycj-2024-0217

王武^{1, 2,},
杨军^1, ,,
王安宝²,
李胜杰¹

1.
清华大学土木工程系, 北京 100084
2.
军事科学院国防工程研究院, 北京 100036

详细信息

作者简介:
王　武（1985－　），男，博士研究生，工程师，w-wang21@mails.tsinghua.edu.cn

通讯作者:
杨　军（1974－　），男，博士，研究员，junyang@tsinghua.edu.cn

中图分类号: O385
计量
- 文章访问数: 110
- HTML全文浏览量: 11
- PDF下载量: 51
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-02
- 修回日期: 2024-09-15
- 网络出版日期: 2024-09-19

Resistance equation of projectile penetrating into reinforced concrete shield

WANG Wu^{1, 2
,},
YANG Jun^{1
, ,},
WANG Anbao²,
LI Shengjie¹

1.
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
2.
Institute of Defense Engineering, AMS, PLA, Beijing 100036, China

摘要

摘要: 为研究弹体在侵彻钢筋混凝土受到阻力的问题，分析了现有钢筋有限长度固支梁理论模型局限，根据钢筋屈服准则研究和耗能分析，提出了弹体直接命中钢筋剪切-塑性铰链模型，以及弹体与钢筋侧面接触时的塑性弦模型，通过耗能分析得到了弹体直接阻力函数；以空腔膨胀理论模型为基础，根据弹体侵彻深度经验公式计算结果，得到了钢筋间接影响下混凝土阻力方程。通过与已有试验数据对比，验证了理论模型的合理性。通过分析钢筋屈服强度、直径、网眼尺寸等配筋方式，以及弹体命中部位对遮弹层抗侵彻性能的影响，给出了遮弹层配筋设计建议：相邻两层钢筋网错孔设置；钢筋网眼与弹体直径比值宜设为0.5～0.8；应结合钢筋极限塑性应变进行高强钢筋选择。
- 钢筋混凝土 /
- 侵彻阻力 /
- 理论模型 /
- 配筋设计
Abstract: To study the penetration resistance to the projectile by the reinforced concrete, the mechanical response of reinforcing bars under the dynamic constraint of both the projectile and concrete was analysed and the limitation of existing finite-length rigid beam models have been obtained. Based on this foundation, a shear-plastic hinge model was used to analyze the case of a projectile directly hitting the reinforcing bars, and a plastic string model was used to analyze the case of a projectile colliding with the side of the reinforcing bars, resulting in a more accurate equation for penetration resistance. In the shear plastic hinge model, stress analysis was performed based on the shear sliding of the reinforcing bar before fracture, and energy dissipation was calculated based on the deformation of the plastic hinge after the reinforcing bar fractures. In the plastic string model, the yield criterion of reinforcing bars under the combined action of bending moment and axial force was analyzed, and the plastic energy dissipation equations for reinforcing bar tension and bending were established. At the same time, the influence of changes in reinforcing bar kinetic energy was considered. Based on the theoretical model of cavity expansion and the empirical formula for the depth of projectile penetration, the concrete resistance equation under the indirect influence of steel reinforcement was obtained. By comparing with existing experimental data, the rationality of the theoretical models was verified. By analyzing the yield strength, diameter, mesh size of reinforcing bars, as well as the impact location of projectile, suggestions for the reinforcement design of the bulletproof layer were given. The adjacent two layers of reinforcing bars mesh should be staggered. The ratio of steel mesh to projectile diameter should be set between 0.5 and 0.8. It is not advisable to simply pursue high-strength reinforcing bars, and the ultimate plastic strain of reinforcing bars should also be considered as an important factor.
- reinforced concrete /
- penetration resistance /
- theoretical model /
- reinforcement design

HTML全文

图 1 弹体与钢筋接触方式^[15]

Figure 1. Contact method between projectile and reinforcing bar^[15]

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图 2 钢筋受力示意图

Figure 2. Schematic diagram of reinforcing bar under dynamic load

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图 3 尖卵头刚性弹剖面示意图

Figure 3. Schematic diagram of oval shaped projectile

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图 4 塑性铰等效长度

Figure 4. Equivalent length of plastic hinge

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图 5 塑性铰链变形示意图

Figure 5. Schematic diagram of plastic hinge deformation

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图 6 钢筋受弯矩作用屈服时横截面应力分布

Figure 6. Cross section stress distribution of reinforcing bar under bending moment action

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图 7 钢筋受弯矩和轴力共同作用屈服时横截面应力分布

Figure 7. Cross section stress distribution of reinforcing bar under combined bending moment and axial force

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图 8 弯矩-轴力共同作用下钢筋屈服面

Figure 8. Yield surface of reinforcing bar under the combined action of bending moment and axial force

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图 9 钢筋塑性变形区示意图

Figure 9. Schematic of plastic deformation zone of reinforcing bar

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图 10 弹体侵彻计算流程图

Figure 10. Flow chart of projectile penetration calculation

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图 11 侵彻试验后部分靶板及钢筋破坏形态^[30]

Figure 11. Partial target plate and reinforcing bars failure morphology after penetration test^[30]

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图 12 弹体减加速度计算结果

Figure 12. Calculation results of projectile deceleration

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图 13 单层钢筋网耗能计算结果

Figure 13. Calculation results of energy consumption for single-layer reinforcing bar mesh

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表 1 钢筋混凝土靶侵彻试验工况及结果

Table 1. Test conditions and results of reinforced concrete target penetration test

靶板编号	计划撞击点位置	配筋方式/mm	弹体质量/g	弹体初速度/(m·s⁻¹)	侵彻深度/mm
靶板编号	计划撞击点位置	配筋方式/mm	弹体质量/g	弹体初速度/(m·s⁻¹)	试验结果^[30]	理论计算结果	相对误差/%
#1	网眼中心	$ \varnothing $10@75	4914	439	568	523	7.92
#2	钢筋交叉点	$ \varnothing $10@75	4920	439	546	503	7.88
#3	网眼中心	$ \varnothing $6.5@30	4968	430	552	517	6.34
#4	钢筋交叉点	$ \varnothing $6.5@30	4962	431	—	501	—

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表 2 弹体侵彻钢筋混凝土靶部分影响参数

Table 2. Impact parameters of projectile penetration into reinforced concrete targets

γ_vol/%	2b/mm	s_h/mm	s_h/2a	γ_vol/%	2b/mm	s_h/mm	s_h/mm	γ_vol/%	2b/mm	s_h/mm	s_h/mm
4	10	26.18	0.17	5	12	30.16	0.2	6	14	34.21	0.23
	12	37.7	0.25		14	41.05	0.27		16	44.68	0.3
	14	51.31	0.34		16	53.62	0.36		18	56.55	0.38
	16	67.02	0.45		18	67.86	0.45		20	69.81	0.47
	18	84.82	0.57		20	83.78	0.56		22	84.47	0.56
	20	104.72	0.7		22	101.37	0.68		24	100.53	0.67
	22	126.71	0.84		24	120.64	0.8		26	117.98	0.79
	24	150.8	1.01		26	141.58	0.94		28	136.83	0.91
注：$ {\gamma }_{\text{vol}} $为体积配筋率，2b为钢筋直径，s_h为钢筋网眼大小。

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