Material Joining and Beam Bending Lab 5 Autumn Quarter

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

Differences in Deflection Although the beams have the same cross-sectional area, the moments of inertia are different Because the moments of inertia are different, the beams deflect different amounts Autumn Quarter

Moments of Inertia A larger moment of inertia means that the beam will be more resistant to deflection I = Area Moments of Inertia (depends on object shape) b h Instructor: B=base H=height These values depend on the orientation of the object and the direction of the force that’s being applied. If the box on the left were rotated 90 degrees, the height would now be larger and the base would be smaller. The example on the right shows a hollow box-shaped tube. This is beneficial because it has much less material than a solid shape, but preserves much of the moment of inertia of the larger box. Autumn Quarter

Stress and Strain: Simple Definitions (lb/inch2) A (cross-sectional area) P (applied force) L (original length) d (deflection from original length) Instructor: Strain is the change in length divided by the total length and is unitless. Stress is the Force per unit of cross sectional area and uses units such as lb/inch^2 or kg/m^2. Autumn Quarter

Stress and Strain: Simple Definitions Stress vs. Strain Curves: Young’s Modulus (slope of curve or material stiffness) Linear Portion (Hooke’s Law): Strain: Stress: (lb/inch2) Instructor: Stress and Strain are linearly related to each other by Hooke’s law. Young’s Modulus is a stiffness constant that relates stress and strain, and is a property of the material. The curve shows stress versus strain for different types of materials. Each material has a linear region called the elastic region. The slope of those lines are determined by Young’s Modules. As stress increases, the material enters a plastic region, which means that the material will deform and no longer return to its original shape completely when stress is removed. The curves end abruptly when the material breaks. Note that the ceramic material breaks before entering the plastic region, and steel has a higher Young’s Modulus than aluminum. Autumn Quarter

Cantilever Beam Bending Equation In this lab, you will measure the deflection d for various loads P. Using this information and other measurements, calculate Young’s modulus E for each beam. P L s y x Instructor: This is a sketch of the test setup. The equation shown can be used to calculate Young’s modulus from the deflection caused by adding weights to the beam. Make sure the dial indicator is positioned vertically and the beam is clamped securely to the table. Autumn Quarter

Material Joining A separate demonstration will be given on the welding procedure The final product will form a ‘T’ shape Instructor: Another way to increase the moment of inertia of a material is to weld two pieces together to form a stronger shape. Students will practice welding PVC together as instructed by the TA’s. This skill will be useful during the robot construction for those teams that wish to use PVC sheets to construct their chassis. Autumn Quarter

Things to Consider: How will joining the beams through welding affect the overall stiffness? Is there any advantage to choosing a more flexible material such as aluminum over a stiffer material such as steel? Hypothetically, if you were to design a 9x9” robot spring quarter, which materials do you feel would be most suited for use? Which shapes would form a stiffer chassis? Instructor: These questions should be discussed in their lab reports. Autumn Quarter

Questions ? Autumn Quarter