求解钢板的对接焊缝强度计算---**Question Stem:**
【例题】试试验算图中所示钢板的对接焊缝的强度, 图中 a=540mm, t=22mm, 轴心力的设计值为N=2150kN。钢材为Q235-B, 手工焊, 焊条为E43型, 三级质量的焊缝, 施焊时加引弧板。
**Chart/Diagram Description:**
* **Title:** 图 对接焊缝的轴心受力情况 (Figure: Axial force condition of butt welds)
* **Type:** Engineering diagrams illustrating two types of butt welds (direct and skew) under axial tensile load. Each type includes a top view and a side view.
* **(a) 对接直缝 (Direct Butt Joint):**
* **Top View:** Shows a rectangular steel plate. A thick vertical line in the center represents a direct butt weld. Two inward-pointing arrows, labeled 'N', are at the left and right ends, indicating an axial tensile force. The width of the plate is labeled 'd', and the length of the plate segment (presumably one side of the weld) is labeled 'a'.
* **Side View:** Shows a thinner rectangular plate, representing the side profile. A vertical weld is shown in the middle. Two inward-pointing arrows, labeled 'N', are at the left and right ends. The thickness of the plate is labeled 't'.
* **(b) 对接斜缝 (Skew Butt Joint):**
* **Top View:** Shows a rectangular steel plate. A thick diagonal line in the center represents a skew butt weld. An arrow along the weld indicates its direction. Two inward-pointing arrows, labeled 'N', are at the left and right ends, indicating an axial tensile force. An angle 'θ' is marked between the diagonal weld line and the horizontal axis (perpendicular to the applied N force direction). The width of the plate is labeled 'd', and the length of the plate segment is labeled 'a'.
* **Side View:** Shows a thinner rectangular plate, representing the side profile. A vertical weld is shown in the middle. Two inward-pointing arrows, labeled 'N', are at the left and right ends. The thickness of the plate is labeled 't'.
**Other Relevant Text (Solution/Explanation):**
解: 直缝连接其计算长度 lw=540mm, 焊缝正应力为:
σ = N / (lw * t) = 2150 × 10³ / (540 × 22) N/mm² = 181 N/mm² > f_t^w = 175 N/mm²
不满足要求, 改用对接斜缝, 取截割斜度为 1.5 : 1, 即θ=56°, 焊缝长度为:
lw = a / sinθ = 54 / sin56° = 65cm
故此时焊缝的正应力为:
σ = Nsinθ / (lw * t) = 2150 × 10³ × sin56° / (650 × 22) N/mm² = 125 N/mm² < f_t^w = 175 N/mm²
剪应力为:
τ = Ncosθ / (lw * t) = 2150 × 10³ × cos56° / (650 × 22) N/mm² = 84 N/mm² < f_v^w = 120 N/mm²
当θ≤56°时, 焊缝强度满足要求。
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钢板对接焊缝是钢结构中最重要的连接方式之一。根据焊缝与受力方向的关系，主要分为对接直缝和对接斜缝两种类型。对接直缝的焊缝方向垂直于轴向受力方向，而对接斜缝则与受力方向成一定角度。为确保结构安全，必须对焊缝进行强度验算。
现在分析题目给定的具体条件。钢板长度a等于540毫米，厚度t等于22毫米，轴心力设计值N等于2150千牛。钢材采用Q235-B，焊条为E43型，焊缝质量为三级。根据规范，三级质量焊缝的抗拉强度设计值为175牛每平方毫米，抗剪强度设计值为120牛每平方毫米。
现在进行对接直缝的强度计算。对接直缝的计算长度等于钢板长度，即540毫米。根据公式，正应力等于轴心力除以焊缝有效截面积。代入数值计算得到应力为181牛每平方毫米。将此值与焊缝抗拉强度设计值175牛每平方毫米比较，发现181大于175，不满足强度要求，需要改用其他方案。
由于直缝不满足强度要求，改用对接斜缝设计。选择斜度为1.5比1，即正切值为1.5。通过反正切函数计算得到角度约为56度。根据几何关系，斜缝长度等于钢板长度除以角度的正弦值，计算得到斜缝长度为650毫米。这样增加了焊缝的有效长度，有助于降低焊缝应力。
对于斜缝，轴向力N需要分解为两个分量来分析。垂直于焊缝方向的分量N乘以sin θ产生正应力，平行于焊缝方向的分量N乘以cos θ产生剪应力。正应力公式为N sin θ除以焊缝有效截面积，剪应力公式为N cos θ除以焊缝有效截面积。这种分解方法是斜缝强度计算的理论基础。