PLEASE SOLVE FOR PART B AND C Learning Goal:

To apply the flexure formula to beams under load and find unknown stresses, moments, and

forcos.

For straight members having a constant cross$-$section that is symmetrical with respect to an

axis with a moment appliod porpendicular to that axis, the maximum normal stress in the cross.

section can be calculated using the flexure formula:

${}_{\text{m}\text{a}\text{x}}=\frac{Mc}{\text{I}}$

where $M$ is the magnilude of the intemal moment with respect to the neutral axis, $c$ is the

perpendieular distance from the neutral axis to the peirt farthest from the neutral axis, and I is

the moment of inertia of the cross$-$section about the neutral axis. The maximum normal stress

will always occur on the top or boltom surface of the beam; in fact, one of these surfaces will

experience a maximal tensile stress while the other experiences the same magnitude of stress

in compression.

For points not on a surlace of the beam, we can use

$\frac{{}_{\text{m}\text{a}\text{x}}}{c}=-\frac{}{y}$

to rowrito tho floxuro formula in the moro goneral form

$=-\frac{M_y}{\text{I}}.$

Part A $-$ Moment Required to Produce a Given Stress

The cross$-$section of a wooden, built$-$up beam is shown below. The dimensions are $L=160mm$ and $w=15mm.$

$($Elgure $1)$

Determine the magnitude of the moment $M$ that must be applied to the beam to create a compressive stress of ${}_D=24$MPa at point $D.$ Also calculate the maximum sitress

developed in the beam. The moment $M$ is applied in the vertical plane about the geometric center of the beam.

Express your answers, separated by a comma, to three significant figures.

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$M=,{}_{\text{m}\text{a}\text{x}}=16\mathrm{.}2,28\mathrm{.}5kN*m,$MPa

Previous Answers

Correct

Term $1$: Correct answer is shown. Your answer $16\mathrm{.}194$ was either rounded differently or used a different number of significant figures than required for this part.

Notice how using both forms of the flexure formula simplifies this otherwise$-$lengthy calculation.

Part B $-$ Minimum Allowable Cross$-$Section

The rod shown in the figure below is supported by smooth journal bearings at A and $B$ that exert only vertical reactions on the shaft.

$($Fiqure $2)$

Determine the smallest allowable diameter of the rod, $d,$ if $z=1\mathrm{.}4m,w_0=14\mathrm{.}2k\frac{N}{m},$ and the maximum alowable bending stress is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=160$MPa.

Express your answer to three significant figures and include the appropriate units.

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Part C $-$ Absolute Maximum Bending Stress

Find the absolute maximum bending stress in the beam shown in the figure below.

$($Figure $3)$

The beam has a square cross$-$section of $5\mathrm{.}0in.$ on each side, is $16ft$ long, and the initial value of the distributed load is $w_0=475l\frac{b}{f}t.$

Express your answer to three significant figures.

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