Problem $1$

An overhung beam with length L supports a uniform distributed load of q $,$ as shown in Figure $1.$

The supports are at a distance d from one another, placed symmetrically with respect to the

beam. The cross$-$section of the beam and its orientation are also shown in the figure.

Figure. $1$: Overhung beam and corresponding cross$-$section $($dimensions for the latter in mm$).$

$($a$)$ Given the geometry, loads and supports, find shear force and bending moment diagrams

for the beam using the graphical method. Comment on the resulting values for the

maximum $($the positive moment with the largest absolute value$)$ and minimum $($the

negative moment with the largest absolute value$).$ 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.

$($b$)$ Calculate the maximum tensile and compressive bending stresses in the beam and indicate

the location along the length of the cross$-$section$($s$)$ where they occur and on what points

of the corresponding cross$-$section$($s$).$

Question $12$ pts

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

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Flag question: Question $2$

Question $22$ pts

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

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Flag question: Question $3$

Question $32$ pts

Find the maximum value of the moment diagram. $($answer in kN$*$m$)$

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Flag question: Question $4$

Question $42$ pts

Find the minimum value of the moment diagram. $($answer in kN$*$m$)$

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Flag question: Question $5$

Question $51\mathrm{.}5$ pts

Find 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 $6$

Question $61\mathrm{.}5$ pts

Find 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 $7$

Question $71\mathrm{.}5$ pts

Find 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 $8$

Question $81\mathrm{.}5$ pts

Find 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 $9$

Question $92$ pts

$$Find the moment of inertia about the neutral axis. $($answer in mm$^4)$

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Flag question: Question $10$

Question $102\mathrm{.}5$ pts

Calculate the maximum tensile stress in the beam. $($answer in MPa$)$

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Flag question: Question $11$

Question $112$ pts

Calculate the location where the maximum tensile stress in the beam occurs. $($answer in m$)$

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Flag question: Question $12$

Question $122\mathrm{.}5$ pts

Calculate the maximum compressive stress in the beam. $($answer in MPa$)$

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Flag question: Question $13$

Question $132$ pts

Calculate the location where the maximum compressive stress in the beam occurs. $($answer in m$)$

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