Structures and stress BaDI 1

Outline Beam Strength and Deflection Moment of Inertia Types of Forces Applied Young’s Modulus (stress and strain) Optimization

Beam Deflection Every object acts as a spring – it will deflect when a force is applied The extent of deflection depends on the force applied, material properties and object shape

Differences in Deflection The beams have the same cross-sectional area, but the shapes and moments of inertia are different With the same volume of material, the hollow beam is stronger (higher moment of inertia).

Types of Forces on a Bending Beam Top of beam – under tension Bottom of beam – under compression

Compression, Tension, and Torsion Reference: http://www.diydoctor.org.uk

Design Optimization Engineering is not about building the strongest possible bridge Engineering is about building a bridge that is strong enough and balances cost, strength, time required to build, etc Engineering is about trade-offs and meeting design specifications

Bending of a Cantilever Beam Experimental setup: L Dial indicator s Weights d

Bending of a Cantilever Beam The deflection of the beam depends on: The load F. More deflection with larger load. The length of the beam. The deflection of the end increases with the length. Material stiffness. Higher stiffness produces less deflection. The geometry of the cross section. Higher moment of inertia results in less deflection.

Bending of a Cantilever Beam Theoretically, the deflection of the beam at the location of the dial indicator is given by Where E is the modulus of elasticity of the beam’s material, and I is the moment of inertia of the cross section.

Moment of Inertia A measure of the way the mass is distributed in a solid

Summary Beam strength depends on force applied, material properties and object shape Important material properties include moment of inertia and Young’s Modulus (stress and strain) Three types of forces are compression, tension, and torsion