HW-3 Problems.pdf C secure https:/M u/bbcswebdav/pid-1174 074- dt-content-rid-58
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HW-3 Problems.pdf C secure https:/M u/bbcswebdav/pid-1174 074- dt-content-rid-5846176 1/courses/M1173-CE-2110-001.002/HW-3%20Problems.pdf ms.uconn.ed PROBLEM 3.125 240 mm A blade held in a brace is used to tighten a screw at A. (a) Determine the forces exerted at B and C, B 240 mm knowing that these forces are equivalent to a force- k couple system at A consisting of R (25 N)i R,j Rzk and M (13.5 N.mi. (b) Find the C k corresponding values of Ry and R (c) What is the 150 mm orientation of the slot in the head of the screw for which the blade is least likely to slip when the brace r is in the position shown? Cri 5Explanation / Answer
a) Equivalence requires ======> Sum(F) =====> R = B + C
-25N i^ + Ry j^ + Rz k^ = -Bk + (-Cx i^ + Cy j^ + Cz k^)
Equating coefficients, -25 = -Cx ==========> Cx = 25 N
Also, Sum(MA) =====> MAR = rB/A x B + rC/A x C
-13.5 i^ = (0.24 i^ + 0.18 j^) x (-B) k^ + (0.48)i^ x [-25 i^ + Cy j^ + Cz k^]
Equating coefficients, -13.5 = -0.18 B =====> B = 75 N
0 = 0.48Cy ====è Cy = 0
And 0 = 0.24*75 – 0.48*Cz =======> Cz = 37.5 N
B = -75 N k^
And C = -25 N i^ + 37.5N k^
b) Now we have for the equivalence of forces
-25 i^ + Ry j^ + Rz k^ = -75 k + [-25 i^ + 37.5 k^]
========> Ry = 0
Rz = -75 + 37.5 = -37.5 N
c) First note that R = -25N i^ - 37.5N k^.
Thus the screw is best able to resist the lateral force Rz when the slot in the head of the screw is vertical.
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