Meriam, Kraige & Bolton — Statics of Particles: Problem 2_101

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/101 Compression member is used to hold up the rectangular plate. If the compressive force in the member is for the position shown, determine the magnitude of the projection of this force (as it acts at point ) along diagonal . Problem 2/101 1. Coordinate System and Points of Interest We establish a 3D coordinate system with the origin at point . Based on the geometry of the rectangular plate and the dimensions provided: The plate has a width of and a length of . One edge of width lies in the plane at an angle of with the . Let the other corner of this edge be . The length of the plate is parallel to the . Thus, corner is: Point lies on the edge , at a distance of from (since it is from ): Point is on the plane (). From the dashed lines, its -coordinate is and its -coordinate is : 2. Force Vector Determination The force acts at point . Since member is in compression, it exerts a force on in the direction from toward . ● Vector from to : AB325×500-mm 320 N AOC O w=325 mmL=500 mm 325 mmx-z30 ∘ x-axis D r = D 325cos30i+ ∘ 0j+325sin30k≈ ∘ (281.45i+162.5k) mm 500 mmy-axisC r = C 281.45i+500j+162.5k mm ADC320 mmD180 mm C r = A r + D 320j=(281.45i+320j+162.5k) mm Bx-yz=0x 410 mmy100 mm r = B (410i+100j+0k) mm FAABA BA BA r = BA r − A r = B (281.45−410)i+(320−100)j+(162.5−0)k ● Magnitude of : ● Force Vector : 3. Unit Vector along Diagonal The diagonal of the plate starts at origin and ends at corner . ● Vector : ● Magnitude of : ● Unit V