Repeat Problem 10-1 taking the stress concentration at the keyway shown in Figure P103 into acco

Repeat Problem 10-1 taking the stress concentration at the...

Key Concepts

Safety and Design Factors

Using appropriate safety factors in design accounts for uncertainties such as material inconsistencies, unexpected load variations, and localized stress concentrations. When stress concentrations from features like keyways are considered, it allows for the adjustment of design parameters to prevent failure under service conditions.

Stress Analysis in Component Design

Stress analysis involves determining the distribution and magnitude of stresses within a component when subjected to external loads. Incorporating factors like stress concentration ensures that the analysis accurately reflects the increased stresses due to geometric features, leading to a safer and more reliable design.

Stress Concentration

Stress concentration refers to the phenomenon where localized increases in stress occur due to abrupt changes in the geometry of a component, such as holes, notches, grooves, or keyways. Understanding and quantifying these local stress peaks is essential because they can lead to material failure even if the overall average stress is within acceptable limits.

Keyway Effects in Mechanical Components

A keyway is a slot or groove cut into a shaft or hub to facilitate the transfer of torque between components. However, the presence of a keyway introduces a geometric discontinuity that intensifies stress in its vicinity. Recognizing and accounting for the stress concentration at a keyway is crucial for ensuring the structural integrity and durability of the design.

Transcript

00:01 In this problem, glider is connected to a hanging mass with the help of an inextensible light string and the string passes over a pulley.

00:13 The glider slides over an inclined surface which has angle of inclination of 10 degree.

00:19 Mass of the glider and mass of the hanging mass is given.

00:24 So we have to draw force diagram for glider and hanging mass and then we have to find acceleration for each of the.

00:31 Blocks so what are the forces that will be acting on the glider first one will be the normal reaction that will be because of the surface the second one will be weight of the glider that will be capital m g and the third one will be the tension force that the string will exert along the string now what will be the forces that will be acting on the hanging mass one will be the weight of the hanging mass that is m g and the second one will be the tension force that will be exerted by the string on the mass.

01:09 So if we draw, if we go to draw force body diagram for glider, so basically there is a tension force which is acting along the plane.

01:25 And the second one is the normal reaction.

01:29 So this is the normal reaction.

01:31 And the third one will be the weight, that is m capital m.

01:36 Into g now what will be the angle so this angle will be theta that is 10 degree all right so mg will have two component one in the direction along the plane and this component will be mg sine theta that is sine 10 and the perpendicular component will be mg cost 10 or cost theta now if we go to draw free body diagram for hanging mass so for the case of hanging mass, two forces are present.

02:17 First is weight of the mass, that is mg, and the second one is the tension force that string will exert.

02:27 So these are the forces.

02:30 Now in b part, we have to find acceleration because acceleration of each block.

02:36 So let us consider that these masses are moving with acceleration a.

02:42 So the glider will be accelerated along the plane towards by the string...

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