Skip to content
Mathify
此计算器目前以英文显示，翻译正在准备中。

物理

已验证计算器，公式透明

物理

Bending Stress Calculator.

Calculates the maximum bending stress in a beam under a point load, based on load, span, and section modulus.

结果随输入实时更新。
ƒ

您的输入

工作原理

  1. 1

    Enter the point load applied at the center of the beam.

  2. 2

    Enter the span length between supports.

  3. 3

    Enter the section modulus of the beam cross-section.

  4. 4

    The calculator computes the maximum bending stress using the formula.

(load * span) / (4 * section_modulus)

常见问题

What is bending stress?

Bending stress is the internal stress that resists bending in a beam. It is maximum at the top and bottom surfaces of the beam.

Why is the formula divided by 4?

For a simply supported beam with a central point load, the maximum bending moment is (load × span) / 4. Dividing by the section modulus gives the stress.

What units should I use?

Use consistent units: newtons for load, millimeters for span, and cubic millimeters for section modulus. The result will be in megapascals (MPa).

浏览此计算器类别

物理浏览全部

结果

公式已检查

Maximum Bending Stress

10MPa

询问任何问题

估算仅供参考——重要决策请咨询专业人士。

工作原理

Calculates the maximum bending stress in a beam under a point load, based on load, span, and section modulus.

  1. Enter the point load applied at the center of the beam.
  2. Enter the span length between supports.
  3. Enter the section modulus of the beam cross-section.
  4. The calculator computes the maximum bending stress using the formula.

公式

此计算器背后的数学公式，供您核对结果。

Bending Stress Formula

σ = M / S

Bending stress equals the bending moment divided by the section modulus.

Example:

Input: M = 500,000 N·mm, S = 50,000 mm³

Calculation: 500,000 / 50,000

Result: 10 MPa

实际应用场景

此计算在日常生活中的应用。

Beam Design

Check if a beam can safely carry a load without exceeding its material's yield strength.

Example: Select a steel beam with sufficient section modulus.

Structural Analysis

Evaluate existing structures for load capacity.

Example: Assess a bridge girder under a heavy vehicle.

Mechanical Components

Design shafts, levers, and frames that experience bending.

Example: Calculate stress in a bicycle crank arm.

提示与常见错误

Tips

  • Use consistent units to avoid conversion errors.
  • For distributed loads, use a different formula.
  • The section modulus depends on cross-section shape; for a rectangle it is (b×h²)/6.
  • Always compare the calculated stress with the material's allowable stress.

Common Mistakes to Avoid

  • Using the wrong bending moment formula for the load case.
  • Forgetting to convert units (e.g., using meters instead of millimeters).
  • Using the area moment of inertia instead of the section modulus.

假设与限制

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.