Question #196482

A distributed load of w N/m is applied over an entire length of a simply supported beam 8m long. The beam section is made up of four 20mmx100mm rectangles arranged as shown. A. Determine the maximum value of w without exceeding the permissible flexure stress of 10MPa. B. Determine the maximum value of w without exceeding the permissible shear stress of 1.2MPa.C. Determine the maximum value of w without exceeding the permissible screw strength of 800N for a pitch of 75mm. *

Expert's answer

"\\sum N_A\\varOmega=0"

"w\\times8\\times4-R_B\\times8=0"

"R_B=4W"

and ,"R_A=R_B=4W"

Moment at any distance "\\eta,"

"N\\eta=4W\\eta-w\\eta,\\frac{\\eta}{2}"

"\\frac{dN}{dm}=4w-w\\eta=0"

"\\eta=4m"

"M_{max}=4W.4-w.4.\\frac{4}{2}"

"=16w-8w=8w"

"M_{max}=8w NM"

"\\tau=\\frac{VA\\bar{y}}{Ib}=\\frac{4w\\times(A\\bar{y_1}+A_2\\bar{y}_2)}{Ib}"

"1.2=\\frac{4w\\times(100\\times20\\times60+40\\times50\\times25}{I\\times 40}"

"I=\\frac{100\\times140^3}{12}-\\frac{2\\times30\\times100^3}{12}=1.786\\times10^7mm"

"1.2=\\frac{4\\times w\\times(100\\times20\\times60+40\\times50\\times25}{1.786\\times10^2\\times40}"

"w=1260.71 N\/m"

"\\frac{VA\\bar{y}}{I}.P"

"\\frac{4w\\times100\\times20\\times60\\times75}{1.786\\times10^7}=2\\times800"

"w=793.78 N\/m"

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