HOW DO I GET $\mathrm{.}409$ m AS MINIMUM HEIGHT FOR h$?$

The beam is supported by a pin at point A and a roller at point $B.$ A distributed load The beam is supported by a pin at point A and a roller at point $B.$ A distributed load

of $W_1=8\frac{kN}{m}$ and an applied force of $F_1=12kN$ are applied to the beam. The

beam has an allowable bending stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=6$MPa. Neglect the weight and

thickness of the beam.

Take the origin for all functions to be at $A.,$ i$.$e$.$ start at the left and go right. Must

use positive sign convention for $V$ and $M.$

Values for the figure are given in the following table. Note the figure may not be to

scale.

Dimensions for the whole beam

Variable Value

$d_1,4m$

$d_2,2m$

Dimensions for the cross$-$section of the beam

Variable Value

$d_1,25mm$

$d_2,125mm$

$d_3,75mm$

a$.$ Determine the magnitude of the vertical support reaction at pin $A,Ay.$

b$.$ Determine the magnitude of the vertical support reaction at roller $B,By.$

c$.$ For the interval $0x4m,$ determine the equation for the Shear Force as a

function of $x,V_{(x)}.$

d$.$ For the interval $0x4m,$ Use integrals to determine the equation for the

Moment as a function of $x,M_{(x)}.$

e$.$ For the interval $4x6m,$ determine the equation for the Shear Force as a

function of $x,V_{(x)}.$

f$.$ For the interval $4x6m,$ Use integrals to determine the equation for the

Moment as a function of $x,M_{(x)}.$

g$.$ Determine the max bending moment on the beam, $M_{\text{m}\text{a}\text{x}}.$ Include negative if

relevant.

h$.$ Determine the minimum height of the beam, $h.$

Round your final answers to $3$ significant digits$/$figures$.$ Do NOT round numbers in

your equations$/$functions$.$

of $W_1=8\frac{kN}{m}$ and an applied force of $F_1=12kN$ are applied to the beam. The

beam has an allowable bending stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=6$MPa. Neglect the weight and

thickness of the beam.

Take the origin for all functions to be at $A.,$ i$.$e$.$ start at the left and go right. Must

use positive sign convention for $V$ and $M.$

Values for the figure are given in the following table. Note the figure may not be to

scale.

Dimensions for the whole beam

Variable Value

$d_1,4m$

$d_2,2m$

Dimensions for the cross$-$section of the beam

Variable Value

$d_1,25mm$

$d_2,125mm$

$d_3,75mm$

a$.$ Determine the magnitude of the vertical support reaction at pin $A,Ay.$

b$.$ Determine the magnitude of the vertical support reaction at roller $B,By.$

c$.$ For the interval $0x4m,$ determine the equation for the Shear Force as a

function of $x,V_{(x)}.$

d$.$ For the interval $0x4m,$ Use integrals to determine the equation for the

Moment as a function of $x,M_{(x)}.$

e$.$ For the interval $4x6m,$ determine the equation for the Shear Force as a

function of $x,V_{(x)}.$

f$.$ For the interval $4x6m,$ Use integrals to determine the equation for the

Moment as a function of $x,M_{(x)}.$

g$.$ Determine the max bending moment on the beam, $M_{\text{m}\text{a}\text{x}}.$ Include negative if

relevant.

h$.$ Determine the minimum height of the beam, $h.$

Round your final answers to $3$ significant digits$/$figures$.$ Do NOT round numbers in

your equations$/$functions$.$