Problem 8 (25 minutes) For the following beam, A=6, B=4, C=2: 1. Determine shear and moment functions V(x) and M(x) in the segment AB (0
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- Problem #2 A wood beam with a square cross section supports the load as shown. Determine the cross sectional dimension in millimeter if the allowable flexure stress is 1000 KPa. Use double integration method. Note: Maximum moment occur at support. 100N/m 100N 1m 4Using the figure above, determine the internal shear and bending moment at pointsA, B, and C (determine just to the left and just to the right of the points if needed).Sketch V (x) and M(x) for the entire beam. Take a = 2 m and b = 1 m. w = 100 N/m. Can you also show me a shear as well as moment diagram? ThanksQuestion 1) F=36 kN single load, M=48 kN.m moment and w=20 kN/m distributed load act on the beamn whose loading condition is given in the figure . The length L is also given as L=3 m. The cross-sectional properties of the beam are; body height y a =210 mm , body thickness x, = 14 mm , flange width xf = 173 mm , flange height yf =14 mm . Point P on the section is located just above the flange-body junction. It is desired to determine the stress state at point Pin the section taken from the B line of the beam. According to this; g w kN/m F kN M kN.m A E В 2L L. L Xf P Yg Xg Question 1-A) B at a point of cutting force (V B ) to find. ( Write your result in kN .) Question 1-B), B at a point of bending moment (M 8 ) you find. ( Write your result in kN.m.) Question 1-C) digits for the decimal part of your result and use the expression E for the decimat part. Write it as 5E-3 instead of 0.005 .) Find the moment of inertia of the beam section .( Do your operations by converting the lengths to…
- The beam supports the loads as shown in the figure. Using E=200 GPa, w = 22 kN/m, P = 35 kN and M = 28 kNm, L1= 2 m, L2 = 5 m, L3= 2 m and a=40 mm. Find, a. by double integration method, the El6 at 1 mn from the right support. b. by double integration method, the maximum El5 between supports c. If w is spread over the entire length and P and Mare interchanged, determine the midspan E15 and deflection by moment - area method. 8a a 10a L1 L2 L3 a За4. A rigid beam fixed at O is loaded by an nth degree spandrel having a vertex at B. a. Determine the shear functions. Use the fixed end as the origin and set rightward and upward as positive directions. Express your answers as V(x)={shear expression} without simplifying {shear expression}. Show all FBDS used b. Draw the shear diagram c. Draw the moment diagram d. If the magnitude of the maximum moment is 20.25kNm, determine the degree of n. 3m 3m A B +x kN 5 no mA Z-shaped rigid bar ABCD, shown in the figure, issuspended by a pin at B, and loaded by a verticalforce P. At A, a 10-mm-diameter steel tie rod AFconnects the section to a firm ground support at F.Use E = 200 GPa. Determine the vertical deflectionat D.
- Problem 1 An angle bracket ABC is restrained by a high strength steel wire CD, and it supports a load P at A, as shown in figure. The strength properties of the wire and the shear pin at B are o, = 350 MPa (wire), and t,=300 MPa (pin at B). If the wire and pin are to be sized to provide a factor of safety of the wire F.S = 3.3 and a factor of safety of the pin F.S = 3.5. What are the required diameters of the wire (to the nearest mm) and the pin (to the nearest mm)? dw D 90 mm B 20° 100 mm View a-a of B P = 2 kNPROBLEMThe beam shown below has internal hinges at points B and D. Assume EI is constant. Using your most convenient methodshow the following:a. Magnitude and directions of the support reactions (Ax,Ay, MA, Cy, Fy). b. The elastic curve.c. Vertical displacement at B. d. Rotation just to the left of B. e. Rotation just to the right of B.3². A cantilever beam carries a vertical load of 150 KN at point B and uniform load of 30 KN/m from C to D., MX a. Draw Shear and Moment Diagrams. b. Using conjugate beam method, solve deflection and slope at B 150KN 4m B 4 m C 30 KN/m 7m D Assume El to be constant: E = 200,000 MPa, I = 500 x 106 mm4.
- 3. A beam is loaded as shown. El is constant. The vertical reactions at B and C are equal to 80kN. For items a, b and c, use the coordinate system shown, with x=0 at point A. a. Derive the moment function, M(x), in terms of El, using Macaulay Functions. b. Derive the slope function, 0(x) in terms of El. С. Derive the deflection function, y(x) in terms of El. The modulus of elasticity is 200 GPa. d. Determine the required moment of inertia, I, if i. The absolute value of the maximum deflection should not exceed 6mm; and ii. The absolute value of the slope should not exceed 0.01 radians at А. 40 kN 40 kN 10 kN/m А В D 2 m 8 m 2 m(b) Figure Q1(b) shows the steel truss with a 3-meter span. The cross-sectional area for all members of the truss is 400 mm?. Span BC carried a uniformly distributed load of 30 kN/m. Prove that the plane truss is internal statically indeterminate. Then, using the Method of Virtual Work, approximate the member forces AC. Assume that member AC is redundant in your analysis. Given Es = 200 GPa. All answers are in three decimal places. B 30kN/m C 4m A 3m FIGURE Q1(b)-; The bending moment M(x) at any section along the span of the cantilever, shown in the figure, is given as: M(x) =- (x -3Lx+2L'). 6L Given that I=3m, q=60KN/m, and EI=6000KN.m², Using a numerical method, find the point at which the bending moment is equal to (-140.5kNm ). (e=1x103)