To calculate the internal normal force, shear force, and bending moment at a point in a beam.

A beam with length L

$=2\mathrm{.}9$m is supported by a pin joint at A and a cable attached at C as shown in $($Figure $1).$ It is subjected to the distributed load with w$1=1\mathrm{.}8$kN$/$m and w$2=2\mathrm{.}6$kN$/$m $.$ The angle between the cable and the beam is $=30.$ Determine the normal force, shear force, and bending moment acting at point B$,$ located x $=0\mathrm{.}9$m to the left of the end of the beam.

Part A

Begin by finding the support reactions for the beam using the free$-$body diagram shown in $($Figure $2).$ What is the tension in the cable?

Express your answer to three significant figures with appropriate units.

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T

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Part B

What is the horizontal reaction force at A

$?$ Assume the forces acts in the direction shown, and use an appropriate sign.

Express your answer to three significant figures with appropriate units.

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Part C

What is the vertical reaction force at A

$?$

Express your answer to three significant figures with appropriate units.

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Part D

Now calculate the internal loading at point B

using the free$-$body diagram of segment BC

$,$ shown in $($Figure $3).$ What is the internal normal force? Assume the force acts as shown, and use the appropriate sign for your answer.

Express your answer to three significant figures with appropriate units.

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NB

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Part E

What is the internal shear force at point B

$?$ Assume the force acts as shown, and use the appropriate sign for your answer.

Express your answer to three significant figures with appropriate units.

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Part F

What is the internal bending moment at B

$?$ Assume the moment acts as shown, and use the appropriate sign for your answer.

Express your answer to three significant figures with appropriate units.

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