For the machine component and loading shown, determine the stress at points A and B when h=2.5 i

For the machine component and loading shown, determine the...

Key Concepts

Stress

Stress is the internal force per unit area that develops within a material when it is subjected to external loads. This concept is central to mechanics of materials as it helps in analyzing how loads are distributed within structural elements, and whether a particular component can safely withstand a given loading condition.

Bending Stress

Bending stress occurs when an external load causes a structural element to bend, leading to a distribution of tensile and compressive stresses across the cross section. It is calculated using the flexure formula, which relates the bending moment acting on the beam, the distance from the neutral axis, and the moment of inertia of the cross-section.

Section Modulus

The section modulus is a geometric property of the cross-section of a structural member, representing its resistance to bending. It is defined as the ratio of the moment of inertia of the section to the distance from the neutral axis to the outermost fiber, and it is used to determine the maximum bending stress in a component.

Load Analysis

Load analysis involves determining how external loads, such as forces and moments, are distributed through a structure. It includes the evaluation of applied loads and their effect on internal forces, which is essential for establishing equilibrium and subsequently calculating stresses at critical points within the component.

Superposition of Stresses

When a component is subjected to multiple types of loads (for example, axial loads and bending moments), the individual stresses resulting from these loads can be combined using the principle of superposition. This allows for the determination of the overall stress at any particular point, accounting for each load's contribution.

Transcript

00:01 For this problem on the topic of analysis of structures, we are given a frame and loading is shown and we are asked to determine the forces or the components of the forces acting on member d -a -b -c at points b and d.

00:15 So we'll first draw a free body diagram of the entire frame and from here we will take anticlockwise moments to be positive and we know that the sum of the moments of all.

00:32 All the forces about point g must equal to zero since the system is in equilibrium.

00:38 So if we take the sum of these moments, this is force h times a distance of 0 .6 meters minus the force of 12 kiloons at a distance of 1 meter minus 6 kiloons at a distance of 0 .5 meters.

01:06 And the sum of these moments must equal to zero.

01:10 So from here we are left with only one unknown, and we get the magnitude of force h to be 25 kiloons, which means that the vector h is 25 kiloons in magnitude and vertically upward in direction.

01:33 So now we can do the same for the free body diagram of the member beh.

01:41 And from here we can take again anti -clockwise moments to be positive and we'll take the sum of moments about point f and we know the sum of these moments must be equal to zero again from equilibrium.

02:06 So the x component of b bx times 0 .5 meters minus 25 kilo -neutons times 0 .2 meters must equal to 0.

02:24 So immediately we can find the magnitude of the x component of b.

02:30 And this is bx, and we get this to be positive 10 kiloons.

02:40 Which means the vector b in the x direction as a magnitude of 10 kiloons...

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