Question

4) Beam AB is subjected to a uniform load of 100 N/m and is supported at B by a post BC shown below. If the coefficient of static friction at B and C are up = 0.2 and Mc = 0.4, determine the force P needed to pull the post out from under the beam. Neglect the weight of the members and the thickness of the post. 100Nm B A 0.7m 0.3 m

Answer 1

100x6N BFB 3 3 NB From above beam Free body Denigram W = wxl Toox 6 Goon AMA- NB X 6 - Goox3=0 NB = 1800/6 300N NB | 300 Assuming B FB Post Slips at B 0.7 Jo.3 > P. Fc <A INC From Above post Free body diagram 71 Fc < McNc FB = MB NB Scanned by TapScanner

+> <Fx = 0 P- FB -Fc=0 +1 <Fy=0 => Nc - 300 = 0 Nc. 2300N 2 + Mc=0 => -px 0-3+ FR-O 2) 3 0.3 but Fo= MB X No 0-2X 300 = 60N Sog => -PX0-3+ 60 = 0 -> 60 200N Pa 0.3 From eq > Fc=P-AB. => 200 60 Fe=140N Scanned by TapScanner

Fc = Me Nc 0.4 x 300 => 120N -(ii) From (i & lig Fc > Fc Slippling At C occurs. So Noto the sume Post Slips At Ci- FB < MB NB Fc = McNc => t Fx = 0 +13 Fy = 0 P-FB-Fc=0 so (a Nc =400 B=0 Px 0.7 + Fc- Fc = Mc XNC => 0.4 x 400 = 160N => Px0o7+ 1600 P= 160 228-57N 0.7 From eq (a - => F8 = P- Fc = 228.57 160 FR = 685+N Scanned by TapScanner

FR MB XNO --> 0-2 x 300 => 60N FB < Fo This case Orawy First Since It requires a smaller value of p P=228.57 N Scanned by TapScanner