# Unit 55

### Unit introduction

All machines and mechanisms consist of interconnected parts working together to produce a desired output. Engineers involved in the design, testing and servicing of mechanical systems need to have a firm grasp of the underpinning principles in order to appreciate the choice of components, the forces acting on them and the way that they relate to each other.

The study of stationary structures and their components is often referred to as ‘statics’. The first two learning outcomes cover the mechanical principles that underpin the design of framed structures, simply supported beams and structural components. The aim is to give learners the means to evaluate the integrity and safety of engineering structures and to lay the foundation for structural analysis at a higher level.

A great many engineering systems are designed to transmit motion and power. These include machine tools, motor vehicles, aircraft and a range of domestic appliances. The study of the motion in mechanical systems is known as ‘kinematics’ and the study of the forces at work and the power they transmit is known as ‘dynamics’. Learning outcomes 3 and 4 aim to extend learners’ knowledge of the mechanical principles associated with these studies. Learning outcome 3 aims to provide a basic knowledge of rotational motion and the effects of centripetal force in simple rotating systems. In learning outcome 4, learners are introduced to simple machines used as lifting devices. An understanding of the mechanical principles involved in the operation of these devices and mechanisms will provide a foundation for the analysis of more complex power transmission systems at a higher level of study.

### Learning outcomes

On completion of this unit a learner should:

• Be able to determine the forces acting in pin-jointed framed structures and simply supported beams
• Be able to determine the stress in structural members and joints
• Be able to determine the characteristics of rotating systems
• Be able to determine the operating characteristics of simple lifting

### Unit content

• Be able to determine the forces acting in pin-jointed framed structures and simply supported beams

Pin-jointed framed structures: solution e.g. graphical (such as use of Bow’s notation, space and force diagram), analytical (such as resolution of joints, method of sections, resolution of forces in perpendicular directions

Forces: active forces, e.g. concentrated loads; uniformly distributed loads (UDL); reactive forces, e.g. support reactions, primary tensile and compressive force in structural members

Simply supported beams: distribution of shear force and bending moment for a loaded beam, e.g. concentrated loads, UDL; types of beam arrangement,

e.g. beam without overhang, beam with overhang and point of contraflexure

• Be able to determine the stress in structural members and joints

Single and double shear joints: fastenings, e.g. bolted or riveted joints in single and double shear; joint parameters, e.g. rivet or bolt diameter, number of rivets or bolts, shear load, expressions for shear stress in joints subjected to single and double shear, factor of safety

Structural members: members, e.g. plain struts and ties, series and parallel compound bars made from two different materials; loading, e.g. expressions for direct stress and strain, thermal stress, factor of safety

• Be able to determine the characteristics of rotating systems

Rotating systems with uniform angular acceleration: systems, e.g. simple (such as rotating rim, flywheel, motor armature, pump or turbine rotor), complex (such as systems where combined linear and angular acceleration is

present, hoist and vehicle on an inclined track); kinetic parameters, e.g. angular displacement, angular velocity, angular acceleration, equations for uniform dynamic parameters,

rotational kinetic energy, application of principle of conservation of energy

Rotating systems with uniform centripetal acceleration: systems, e.g. simple (such as concentrated mass rotating in a horizontal or vertical plane, vehicle on a hump-backed bridge, aircraft performing a loop), complex (such as centrifugal clutch, vehicle on a curved track); kinetic parameters,

• Be able to determine the operating characteristics of simple lifting machines

Parameters of lifting machines: kinetic parameters, e.g. input motion,

output motion, velocity or movement ratio, overhauling; dynamic parameters,

e.g. input effort, load raised, mechanical advantage or force ratio, law of a machine, efficiency, limiting efficiency

Lifting machines: lifting machines, e.g. simple (such as inclined plane, screw jack, pulley blocks, wheel and axle, simple gear train winch), differential (such as differential wheel and axle, Weston differential pulley block, compound gear train winch)