Bending in Two Planes, Lecture notes of Mathematics

Download Bending in Two Planes and more Lecture notes Mathematics in PDF only on Docsity!

Two-Plane Bending

Contents:

1. Introduction

2. Special case- Circular cross-section beams

3. Examples

• Bending in both x-y and x-z planes
• Cross sections with one or two planes of symmetry only
• Two neutral planes in bending
• Resolve external loading in y and z components Bending stress at a point is the algebraic sum of bending stress in x-y and x-z planes: x (^ x )^ (^ x ) y z z y z y

M y^ M z

I I

Introduction

Example 1 .1: A cantilever beam shown below is loaded with a uniform load of 50 lb/in in the x-y plane and a point load of 100 lb in the x-z direction. Find the maximum tensile and the maximum compressive bending stress in the beam. The beam is 8-in long.

Examples

Example 1.2: A shaft carries two pulleys and is supported by frictionless bearings at the ends. The forces acting on the pulleys due to the moving belt are shown below. Calculate the maximum bending stress. The diameter of the shaft is 1.5-in. The diameter of the pulley at B is 4-in and at C is 8 - in.

Examples