Problem $3$

The compound beam shown in Figure $3$ is supported with a pin to the left, a roller to the right and another roller at a distance of $3$ a from the pin. There is also an internal hinge connecting the two sections of the beam.

Given the geometry, loads and supports, find shear force and bending moment diagrams for this beam using the graphical method. Label your diagrams with appropriate numerical values, indicate and quantify maximum and minimum values, and identify the corresponding functional behavior for each segment, i$.$e$.,$ constant, linear, quadratic, etc. Justify the numerical values you use to label your diagrams, i$.$e$.,$ show the calculations you use to apply the graphical method.

Take w$=500$lb$//$ft$,$P$=400$lb$,$M$=200$lb $*$ft$,$ and a$=3$ft$.$

Question $195$ pts

Find the maximum value of the shear diagram $($answer in lb$).$

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Flag question: Question $20$

Question $205$ pts

Find the minimum value of the shear diagram $($answer in lb$).$

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Flag question: Question $21$

Question $215$ pts

Find the maximum value of the moment diagram. $($answer in lb$*$ft$)$

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Flag question: Question $22$

Question $225$ pts

Find the minimum value of the moment diagram. $($answer in lb$*$ft$)$

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Flag question: Question $23$

Question $235$ pts

Which of the following is the correct the shape of the moment diagram for region $1.$

Group of answer choices

Zero

Constant

Linear, Positive Slope

Linear, Negative Slope

Quadratic, Positive Slope, Concave Up

Quadratic, Positive Slope, Concave Down

Quadratic, Negative Slope, Concave Up

Quadratic, Negative Slope, Concave Down

Cubic

None of the Above

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Flag question: Question $24$

Question $245$ pts

Which of the following is the correct the shape of the moment diagram for region $2.$

Group of answer choices

Zero

Constant

Linear, Positive Slope

Linear, Negative Slope

Quadratic, Positive Slope, Concave Up

Quadratic, Positive Slope, Concave Down

Quadratic, Negative Slope, Concave Up

Quadratic, Negative Slope, Concave Down

Cubic

None of the Above

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Flag question: Question $25$

Question $255$ pts

Which of the following is the correct the shape of the moment diagram for region $3.$

Group of answer choices

Zero

Constant

Linear, Positive Slope

Linear, Negative Slope

Quadratic, Positive Slope, Concave Up

Quadratic, Positive Slope, Concave Down

Quadratic, Negative Slope, Concave Up

Quadratic, Negative Slope, Concave Down

Cubic

None of the Above

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Flag question: Question $26$

Question $262\mathrm{.}5$ pts

Which of the following is the correct the shape of the moment diagram for region $4.$

Group of answer choices

Zero

Constant

Linear, Positive Slope

Linear, Negative Slope

Quadratic, Positive Slope, Concave Up

Quadratic, Positive Slope, Concave Down

Quadratic, Negative Slope, Concave Up

Quadratic, Negative Slope, Concave Down

Cubic

None of the above

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Flag question: Question $27$

Question $272\mathrm{.}5$ pts

Which of the following is the correct the shape of the moment diagram for region $5.$

Group of answer choices

Zero

Constant

Linear, Positive Slope

Linear, Negative Slope

Quadratic, Positive Slope, Concave Up

Quadratic, Positive Slope, Concave Down

Quadratic, Negative Slope, Concave Up

Quadratic, Negative Slope, Concave Down

Cubic

None of the Above