Problem 2.3-3 q 3 kN/m F = 7 kN ; L = 12 m A q L B F
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Determine the stress resultants N(x), V(x), M(x) and draw the diagrams of the stress resultants and calculate the extremal values. At first, consider all parameters (F, a, L, ...) as variables and fill in their actual values at the end of your calculation.
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- Solve the preceding problem for sx= 11 MPa and ??y= -20 MPa (see figure).A safety valve on the top of a tank containing steam under pressure p has a discharge hole of diameter d(see figure). The valve is designed to release the steam when the pressure reaches the value Pmax If the natural length of the spring, is L and its stiffness is k, what should be the dimension ft of the valve? (Express your result as a formula for h.)A cylinder filled with oil is under pressure from a piston, as shown in the figure. The diameter d of the piston is 1,80 in. and the compressive force F is 3500 lb. The maximum allowable shear stress t^^, in the wall of the cylinder is 5500 psi. What is the minimum permissible thickness t„± of the cylinder wall? (Sec figure
- A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.3: T = 10.11 kN-mProblem 3. As shown in the Figure below, please determine the internal force in the middle of AB, with the given data: OA-15 cm, OB-30 cm, OC-60 cm. W=40N, Wo=60N. F=1214N, B-10°, FM=1236 N, and 8=15%. Fj B FM W Wo 4
- 2. The tires of an agricultural tractor shown below are assumed to be 25 cm wide for the front tires and 40 cm at the rear tires. Ground contact of each tire is 15 cm. Calculate the compressive stress between each tire and the ground surface. Weight = 2,500 kg 15 cm 1.3m Point A 2.2 m 2R 2FQ2/ A steel bar shown in figure consists of two segments having diameter of AB= 28 mm and BD= 40 mm. Find the stress of the rod BD. 67 KN 600 mm 18 kN Answer 18 kN 450 mm 36 KN 36 kN 300 mm(b) Figure Q1 (b) shows a thin disc mounted on a shaft between two bearings. The thin disc density is not perfectly uniform because it not perfectly manufactured. The thin disc perfectly mounted on the shaft. The thin disc centre of mass is not the same as the centre of rotation. Consider the unbalance thin disc mass (m), centre by a distance (e) and the shaft rotates at a speed (w). The thin disc attached LL meter from left bearing and LR from right bearing. (i) Find the reaction force on the left bearing, FL. (ii) Calculate the reaction force on the right bearing, FR.
- Consider a long cylindrical solid rod - total length L - mass density p; - radius R1 = R2 = R; suspended from the top and hung freely downward along the (-1)Ž direction; - subjected to gravitational pull from the ground in the (-1)Ź direction. R2 +Z Z = h R1 Z = 0 a) Calculate the longitudinal stress o within the rod as a function of h; b) Repeat the calculation ifR| turns into a cone); = 0 and R2 = R (i.e., when the cylindrical rod c) Based on your answers to a) and b), provide some reasoning as to why a space elevator would not work [hint: think about the rod as the load bearing element of the space elevator].1. A tripod shawn supports of note that ball and rocket joints are used to mount the tripuod a load P=1000N at point A. Take at points B,D, and C. consider the t LI L 2 L2: 4 L3 : 3 A : 45° g :30° %3D on x-z plane L2 POINT C (2,-2,3) C0,0,0) ミー- Determine the ff Force of AB - N Force of AC - N Force of AD : NF2 Q1) Axial displacement of point C in the system shown on the left is 0.01 cm. Find the maximum elongation of the bar and the maximum normal stress. A F1 A. GIVEN: F2 = 100 kN, (1 = 240 cm, €2= 160 cm, bi = 5 cm, bz=10 cm, h=5 cm, E=2.107 N/em², a=20 cm Note: neglect stress concentration. h bị b2 A-A section