Problem One: For the beam shown below, determine the flexural stresses, shear stresses,

principal stresses, and the angle to the principle stress plane at the locations shown $($numbered

$1$ through $6).$ Locations $1$ and $2$ are at the top of the beam, while locations $5$ and $6$ are at the

bottom. Location $3$ is at the beam mid$-$height, while location $4$ is midway between locations $3$

and $5.$

Assume that the member is uncracked and apply Mohr$$s circle in your calculations. For the

dead weight of the beam, assume a concrete density of $140$ Lb$/$ft$3,$ and a beam cross section of

$24$ high by $18$ wide. Based on your calculations, would you expect that the beam would

crack at any of the locations due to the applied loads? $($assume f$$c $=4$ksi to calculate concrete

tensile strength which can be taken as $10\%$ of compressive strength$)$ Note: To calculate the

moment and shear demands for flexural and shear stresses, be sure to include the appropriate

load factors, i$.$e$.,1\mathrm{.}2$D$+1\mathrm{.}6$L Problem One: For the beam shown below, determine the flexural stresses, shear stresses, principal stresses, and the angle to the principle stress plane at the locations shown $($numbered $1$ through $6).$ Locations $1$ and $2$ are at the top of the beam, while locations $5$ and $6$ are at the bottom. Location $3$ is at the beam mid$-$height, while location $4$ is midway between locations $3$ and $5.$

Assume that the member is uncracked and apply Mohr's circle in your calculations. For the dead weight of the beam, assume a concrete density of $\backslash (140\backslash$mathrm$\{$Lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ),$ and a beam cross section of $24"$ high by $18"$ wide. Based on your calculations, would you expect that the beam would crack at any of the locations due to the applied loads? $($assume $\backslash ($ f$^\{\backslash$prime$\}\{\}\_\{$c$\}=4\backslash$mathrm$\{$ksi$\}\backslash )$ to calculate concrete tensile strength which can be taken as $\backslash (10\backslash \%\backslash )$ of compressive strength$)$ Note: To calculate the moment and shear demands for flexural and shear stresses, be sure to include the appropriate load factors, i$.$e$.,\backslash (1\mathrm{.}2\backslash$mathrm$\{$D$\}+1\mathrm{.}6\backslash$mathrm$\{$~L$\}\backslash )$

$\backslash [$

$\backslash$mathrm$\{$L$\}=385\backslash$mathrm$\{$Lb$\}/\backslash$mathrm$\{$ft$\}$

$\backslash ]$