Sailing enthusiast is seeking materials for lightweight

Assignment Help Mechanical Engineering

Reference no: EM13708539

A sailing enthusiast is seeking materials for lightweight panels to use in a sea-going yacht. The panels are of rectangular cross-section and will be loaded in bending, as shown in Figure 1. The span L and width b of the panels are fixed, but the thickness d may vary (up to a maximum specified value). The required stiffness is specified as a maximum allowable deflection? under a given central load W, for a simply supported span. The designer is interested in two scenarios: (i) minimum mass; (ii) minimum material cost.

NB: The central deflection of a simply supported span under a point load is given by:

?= (WL^3)/48 EI where I= bd^3/12

a) Show that the stiffness and geometric constraints lead to the relationship Ed^3 = constant, where E is Young’s modulus. Explain why the design specification leads to a minimum allowable value for E, and find an expression for this minimum value.

b) Write down an expression for the first objective to be minimised (mass) and use the stiffness constraint to eliminate the free variable (thickness). Hence define the material performance index to maximise for a minimum mass design.

c) How does the short-list of materials in (c) change if the limit on depth leads to a requirement for a minimum required Young's modulus of 5 GPa?

Reference no: EM13708539

Questions Cloud

How does its final potential energy compare : A horizontal spring, resting on a frictionless tabletop, is stretched 12cm from its unscratched configuration and a 1.00-kg mass is attached to it. How does its final potential energy compare to its initial potential energy

What is the angular momentum of the electron in this state : Consider an ionized carbon atom with only one electron, which is next to the lowest energy state. The atomic number for Carbon is 6. What is the angular momentum of the electron in this state

What would be the work required to increase speed : If the work required to speed up a car from 14km/h to 21km/h is 8.0 × 103 J, What would be the work required to increase the car's speed from 21km/h to 32km/h

Determine the work and heat transfer for the process : Two kilograms of water, initially a saturated liquid at 100 kPa, are heated to saturated vapor while the pressure is maintained constant. Determine the work and heat transfer for the process, each in kJ.

Sailing enthusiast is seeking materials for lightweight : A sailing enthusiast is seeking materials for lightweight panels to use in a sea-going yacht. The panels are of rectangular cross-section and will be loaded in bending, as shown in Figure 1. The span L and width b of the panels are fixed, but the thi..

How much more gravitational potential energy hammer have : How much more gravitational potential energy does a 1.8kg hammer have when it is on a shelf 1.4m high than when it is on a shelf 0.90m high

Calculate the mass of a single molecule in the gas : The rms speed of the molecules of a gas at 149Â°C is 209 m/s. Calculate the mass of a single molecule in the gas

Find the rms speed of the molecules of a sample of nitrogen : Find the rms speed of the molecules of a sample of N2 (diatomic nitrogen) gas at a temperature of 38.9Â°C

Rate of moisture addition to the air by adiabatic saturator : In a heating/humidifying system moist air first flows through a heating coil and then through an air washer. The air enters the system at 55 °F dry-bulb temperature and 40 % relative humidity. The air exits the system at 90 °F dry-bulb temperature an..

User Account

All Pages