四点弯曲试验是一种经典的材料力学实验，用于测定材料的弹性模量、弯曲强度等力学性能。对于不同材料，四点弯曲试验的计算公式会有所不同，但基本原理是相似的。以下是几种常见材料在四点弯曲试验中的计算公式：

一、矩形截面样品的计算公式

1. 正应力（抗弯强度）

• 公式：$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">=</span>\frac{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">3</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">(</span>\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">)</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">2</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">2</span>}}}$σ=2bh23P(L?l)

• 其中，$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}$σ 为抗弯强度（MPa）；P 为加载力（N）；L 为下支点跨距（mm）；l 为上支点跨距（mm）；b 为样品宽度（mm）；h 为样品厚度（mm）。

2. 弹性模量

• 公式：$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">=</span>\frac{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">3</span>}}}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">48</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">\Delta </span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}$E=48IΔyPL3

• 其中，E 为弹性模量（MPa）；P 为加载力（N）；L 为下支点跨距（mm）；I 为样品的惯性矩（对于矩形截面，$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">=</span>\frac{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">3</span>}}}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">12</span>}}$I=12bh3，单位：$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">4</span>}}$mm4）；$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">\Delta </span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}$Δy 为样品跨距中点的挠度（mm）。

二、圆形截面样品的计算公式

1. 正应力（抗弯强度）

• 公式：$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">=</span>\frac{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">32</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">(</span>\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">)</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">3</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">3</span>}}}$σ=3πd332P(L?l)

• 其中，$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}$σ 为抗弯强度（MPa）；P 为加载力（N）；L 为下支点跨距（mm）；l 为上支点跨距（mm）；d 为样品直径（mm）。

2. 弹性模量

• 公式：$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">=</span>\frac{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">3</span>}}}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">48</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">\Delta </span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}$E=48IΔyPL3

• 其中，E 为弹性模量（MPa）；P 为加载力（N）；L 为下支点跨距（mm）；I 为样品的惯性矩（对于圆形截面，$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">=</span>\frac{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">4</span>}}}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">64</span>}}$I=64πd4，单位：$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}}^{\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">4</span>}}$mm4）；$\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">\Delta </span>}\mathrm{<span\; style="box-sizing:\; border-box;\; margin:\; 0px;\; padding:\; 0px;\; font-family:\; 宋体,\; SimSun;\; font-size:\; 16px;\; line-height:\; inherit;\; font-weight:\; inherit;\; font-style:\; inherit;\; vertical-align:\; baseline;\; background:\; transparent;\; -webkit-tap-highlight-color:\; transparent;\; appearance:\; none;">?</span>}$Δy 为样品跨距中点的挠度（mm）。

三、其他注意事项

1. 试样尺寸与形状：四点弯曲试验中的试样通常采用矩形或圆形截面，以简化计算和分析。实验前需要准确测量试样的尺寸和重量，并计算其惯性矩。

2. 实验过程：实验过程中，试样被固定在两个支点之间，并在试样中间施加集中载荷。由于载荷的作用，试样发生弯曲变形，形成弯矩和剪力，从而产生拉伸和压缩应力。通过测量试样在载荷作用下的弯曲角度和挠度，可以计算出材料的弹性模量和抗弯强度等力学性能。

3. 实验精度：为了提高实验精度，研究人员通常采用有限元分析等数值方法对实验结果进行校准。此外，实验过程中还需要注意试样的非均匀变形等因素对测量结果的影响。

4. 应用范围：四点弯曲实验可应用于复合材料、新型合金、陶瓷材料等多种材料的力学性能研究，为工程设计提供重要依据。

概括而言，四点弯曲试验的计算公式因材料形状和测试目的的不同而有所差异。在实际应用中，需要根据具体情况选择合适的公式进行计算和分析。