Chapter 5 Torsion

5.5 Statically Indeterminate Torque-Loaded Members Equilibrium equation: TA + TB = T

Compatibility condition Angle of twist of AC: Angle of twist of CB: Solution:

5.6 Solid Noncircular Shafts (skip) 5.7 Thin-Walled Tubes Having Closed Cross- Sections (skip) 5.8 Stress Concentration * Stress concentration occurs at (i) location where cross section changes, or (ii) location where load is applied.

K – torsional stress concentration factor max is used for design

Chapter 6 Bending

6.1 Shear and Moment Diagrams Beam Beam – slender bar, support transverse load

Internal Forces

* Normal force NB – perpendicular to cross-section It tends to stretch or compress the member. * Shear force VB – tangent (parallel) to cross-section It tends to cut the member in transverse direction. * Bending moment MB – couple moment It tends to bend the member.

Sign Convention * Distributed load Upward - positive * N – normal force Tensile – positive Compressive - negative * V – shear force Causing clockwise rotation – positive * M – banding moment Causing concave downward (hold water) – positive

Analysis Procedure * Find support reactions. * If concentrated forces exist, divide the beam into several segments. * Cut each segment in middle, draw FBD, write equilibrium equations, and find shear force and moment. * Draw shear and moment diagrams. Note: Always draw internal forces in positive directions. If the result is negative, the actual direction is opposite.

EXAMPLE 6.1

EXAMPLE 6.1 (CONTINUED)

EXAMPLE 6.3

EXAMPLE 6.4

EXAMPLE 6.4 (CONTINUED)

6.2 Graphical Method for Constructing Shear and Moment Diagrams Regions of Distributed Load * Differential equations: