The rigid beam is supported by three A-36 steel wires, each having a length of 4 ft. The cross-s

The rigid beam is supported by three A-36 steel wires, each...

Key Concepts

Static Equilibrium

Static equilibrium is a fundamental concept in structural mechanics where the sum of forces and the sum of moments acting on a system must both equal zero. This principle is applied to analyze the distribution of loads among the supporting elements and to ensure that the structure remains stable under the applied loading conditions.

Deflection Analysis

Deflection analysis involves calculating the displacement of a structure under load. Even when a beam is assumed to be rigid, the deformations in the supporting elements (such as the elongation of wires) will result in the overall displacement of the structure. This concept is key when assessing serviceability and the performance of a structure as it approaches the yield point of its supporting elements.

Cross-sectional Area and Stress

The cross-sectional area of a structural member is inversely related to the stress it experiences under an applied load, as stress is defined as force divided by area. In problems involving wires or cables, differences in cross-sectional areas can lead to different stress levels for the same force, thereby affecting which member is most likely to yield first.

Distributed Load

A distributed load is a load applied continuously along the length of a structural element, such as a beam. It is typically expressed in units of force per unit length and requires integration over the length of the beam to determine the total applied force. This concept is fundamental in the analysis of beams because it directly influences the internal forces and moments that develop within the structure.

Elastic Perfectly Plastic Behavior

Elastic perfectly plastic behavior describes a material model in which a material responds elastically (reversibly) up to its yield stress, beyond which it deforms plastically at a constant stress level without any additional increase in load. This model is used to predict the onset of yielding and the subsequent permanent deformations in structural elements such as the steel wires in the given problem.

Rigid Beam Assumption

The rigid beam assumption implies that the beam does not deform under loading; that is, its geometry remains unchanged even when subjected to loads. This simplifies the analysis by ensuring that deformations in the supporting elements (in this case, the wires) are responsible for all the structural displacements, allowing for a straightforward relationship between load and displacement.

Yielding

Yielding is the process by which a material begins to deform plastically, meaning that after the load is removed, some of the deformation remains permanently. In structural analysis, determining the yield point is crucial because it marks the limit to which materials can be safely loaded without incurring permanent damage.

Transcript

00:01 In this question it is given that in hydrogen the transition from level 1 to level 2 has a rest wavelength that is 121 .6 nanometer now it is given that we see this line at a wavelength of 125 .1 nanometer in a star that we have to find the velocity of this in the direction of the earth so first of all i am writing the given data for this tuition so we have given original wavelength that is lambda is equal to this is 121 .6 nanometer that is 121 .6 into 10 to the power minus 9 meter and we know that the frequency is given by that is f is equal to this is c by lambda and this is equal to speed of flight there is 3 into 10 to the power 8 upon this is 121 .6 into 10 to the power minus 9 so we can say this is equal to 2 .467 into 10 to 10 to the power 15 harts now we know we have the observed wavelength that is lambda dash this is equal to 121 .1 1 into 10 to the power minus 9 meter and we so from here we can calculate the value of frequency that is f dash and this is equal to c by lambda dash so we can say this will comes out to be 2 .398 into 10 to the power this is 15 harts now we know that from doppler's effect we can say that from doppler's formula that is observed frequency f -dash is equal to this is f into under root of this is c minus v upon this is c plus v here v is the velocity of the observer so we can say that from here the value of c minus v upon this is c plus v and this will come out to be that is f dash upon f whole square now put all the data in this equation which we had calculated so f dash by f is equal to this is 2 .398 into 10 to the power 15 upon this is 2 .467 into 10 to the power 15 whole square so we can say this will comes out to be 0 .945 or we can say that this is equal to c minus v upon this is c plus v now we can say that from here this can be written as this is 0 .945 plus 1 into v is equal to the c into 1 minus 0 .945.

03:30 From here we get the value of v that is 8 .5 into 10 to the power 6 meter per second...

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