1import math
2
3def check_circular_beam_safety(diameter, length, load, material):
4    """
5    检查圆形梁是否可以安全支撑给定载荷
6    
7    参数：
8    diameter (float): 梁直径（米）
9    length (float): 梁长度（米）
10    load (float): 施加载荷（牛顿）
11    material (str): 'steel'，'wood'或'aluminum'
12    
13    返回：
14    dict: 安全评估结果
15    """
16    # 材料属性（MPa）
17    allowable_stress = {
18        'steel': 250,
19        'wood': 10,
20        'aluminum': 100
21    }
22    
23    # 计算惯性矩（m^4）
24    I = (math.pi * diameter**4) / 64
25    
26    # 计算截面模量（m^3）
27    S = I / (diameter / 2)
28    
29    # 计算最大弯矩（N·m）
30    M = (load * length) / 4
31    
32    # 计算实际应力（MPa）
33    stress = M / S
34    
35    # 计算安全系数
36    safety_factor = allowable_stress[material] / stress
37    
38    # 计算最大允许载荷（N）
39    max_allowable_load = load * safety_factor
40    
41    return {
42        'safe': safety_factor >= 1,
43        'safety_factor': safety_factor,
44        'max_allowable_load': max_allowable_load,
45        'stress': stress,
46        'allowable_stress': allowable_stress[material]
47    }
48
49# 示例用法
50beam_params = check_circular_beam_safety(0.05, 2, 1000, 'aluminum')
51print(f"梁是 {'安全' if beam_params['safe'] else '不安全'}")
52print(f"安全系数: {beam_params['safety_factor']:.2f}")
53

1public class IBeamSafetyCalculator {
2    // 材料属性（MPa）
3    private static final double STEEL_ALLOWABLE_STRESS = 250.0;
4    private static final double WOOD_ALLOWABLE_STRESS = 10.0;
5    private static final double ALUMINUM_ALLOWABLE_STRESS = 100.0;
6    
7    public static class SafetyResult {
8        public boolean isSafe;
9        public double safetyFactor;
10        public double maxAllowableLoad;
11        public double stress;
12        public double allowableStress;
13        
14        public SafetyResult(boolean isSafe, double safetyFactor, double maxAllowableLoad, 
15                           double stress, double allowableStress) {
16            this.isSafe = isSafe;
17            this.safetyFactor = safetyFactor;
18            this.maxAllowableLoad = maxAllowableLoad;
19            this.stress = stress;
20            this.allowableStress = allowableStress;
21        }
22    }
23    
24    public static SafetyResult checkIBeamSafety(
25            double height, double flangeWidth, double flangeThickness, 
26            double webThickness, double length, double load, String material) {
27        
28        // 根据材料获取允许应力
29        double allowableStress;
30        switch (material.toLowerCase()) {
31            case "steel": allowableStress = STEEL_ALLOWABLE_STRESS; break;
32            case "wood": allowableStress = WOOD_ALLOWABLE_STRESS; break;
33            case "aluminum": allowableStress = ALUMINUM_ALLOWABLE_STRESS; break;
34            default: throw new IllegalArgumentException("未知材料: " + material);
35        }
36        
37        // 计算工字梁的惯性矩
38        double webHeight = height - 2 * flangeThickness;
39        double outerI = (flangeWidth * Math.pow(height, 3)) / 12;
40        double innerI = ((flangeWidth - webThickness) * Math.pow(webHeight, 3)) / 12;
41        double I = outerI - innerI;
42        
43        // 计算截面模量
44        double S = I / (height / 2);
45        
46        // 计算最大弯矩
47        double M = (load * length) / 4;
48        
49        // 计算实际应力
50        double stress = M / S;
51        
52        // 计算安全系数
53        double safetyFactor = allowableStress / stress;
54        
55        return new SafetyResult(
56            safetyFactor >= 1.0,
57            safetyFactor,
58            maxAllowableLoad,
59            stress,
60            allowableStress
61        );
62    }
63    
64    public static void main(String[] args) {
65        // 示例：检查工字梁的安全性
66        SafetyResult result = checkIBeamSafety(
67            0.2,    // 高度（米）
68            0.1,    // 翼缘宽度（米）
69            0.015,  // 翼缘厚度（米）
70            0.01,   // 腹板厚度（米）
71            4.0,    // 长度（米）
72            15000,  // 载荷（N）
73            "steel" // 材料
74        );
75        
76        System.out.println("梁是 " + (result.isSafe ? "安全" : "不安全"));
77        System.out.printf("安全系数: %.2f\n", result.safetyFactor);
78        System.out.printf("最大允许载荷: %.2f N\n", result.maxAllowableLoad);
79    }
80}
81

1' Excel VBA函数用于矩形梁安全检查
2Function CheckRectangularBeamSafety(Width As Double, Height As Double, Length As Double, Load As Double, Material As String) As Variant
3    Dim I As Double
4    Dim S As Double
5    Dim M As Double
6    Dim Stress As Double
7    Dim AllowableStress As Double
8    Dim SafetyFactor As Double
9    Dim MaxAllowableLoad As Double
10    Dim Result(1 To 5) As Variant
11    
12    ' 根据材料设置允许应力（MPa）
13    Select Case LCase(Material)
14        Case "steel"
15            AllowableStress = 250
16        Case "wood"
17            AllowableStress = 10
18        Case "aluminum"
19            AllowableStress = 100
20        Case Else
21            CheckRectangularBeamSafety = "无效材料"
22            Exit Function
23    End Select
24    
25    ' 计算惯性矩（m^4）
26    I = (Width * Height ^ 3) / 12
27    
28    ' 计算截面模量（m^3）
29    S = I / (Height / 2)
30    
31    ' 计算最大弯矩（N·m）
32    M = (Load * Length) / 4
33    
34    ' 计算实际应力（MPa）
35    Stress = M / S
36    
37    ' 计算安全系数
38    SafetyFactor = AllowableStress / Stress
39    
40    ' 计算最大允许载荷（N）
41    MaxAllowableLoad = Load * SafetyFactor
42    
43    ' 准备结果数组
44    Result(1) = SafetyFactor >= 1 ' 安全？
45    Result(2) = SafetyFactor ' 安全系数
46    Result(3) = MaxAllowableLoad ' 最大允许载荷
47    Result(4) = Stress ' 实际应力
48    Result(5) = AllowableStress ' 允许应力
49    
50    CheckRectangularBeamSafety = Result
51End Function
52
53' 在Excel单元格中的用法：
54' =CheckRectangularBeamSafety(0.1, 0.2, 3, 5000, "steel")
55

1#include <iostream>
2#include <cmath>
3#include <string>
4#include <map>
5
6struct BeamSafetyResult {
7    bool isSafe;
8    double safetyFactor;
9    double maxAllowableLoad;
10    double stress;
11    double allowableStress;
12};
13
14// 计算圆形梁的安全性
15BeamSafetyResult checkCircularBeamSafety(
16    double diameter, double length, double load, const std::string& material) {
17    
18    // 材料属性（MPa）
19    std::map<std::string, double> allowableStress = {
20        {"steel", 250.0},
21        {"wood", 10.0},
22        {"aluminum", 100.0}
23    };
24    
25    // 计算惯性矩（m^4）
26    double I = (M_PI * std::pow(diameter, 4)) / 64.0;
27    
28    // 计算截面模量（m^3）
29    double S = I / (diameter / 2.0);
30    
31    // 计算最大弯矩（N·m）
32    double M = (load * length) / 4.0;
33    
34    // 计算实际应力（MPa）
35    double stress = M / S;
36    
37    // 计算安全系数
38    double safetyFactor = allowableStress[material] / stress;
39    
40    // 计算最大允许载荷（N）
41    double maxAllowableLoad = load * safetyFactor;
42    
43    return {
44        safetyFactor >= 1.0,
45        safetyFactor,
46        maxAllowableLoad,
47        stress,
48        allowableStress[material]
49    };
50}
51
52int main() {
53    // 示例：检查圆形梁的安全性
54    double diameter = 0.05; // 米
55    double length = 2.0;    // 米
56    double load = 1000.0;   // 牛顿
57    std::string material = "steel";
58    
59    BeamSafetyResult result = checkCircularBeamSafety(diameter, length, load, material);
60    
61    std::cout << "梁是 " << (result.isSafe ? "安全" : "不安全") << std::endl;
62    std::cout << "安全系数: " << result.safetyFactor << std::endl;
63    std::cout << "最大允许载荷: " << result.maxAllowableLoad << " N" << std::endl;
64    
65    return 0;
66}
67