Example: The simply supported beam shown is subjected to the concentrated Determine the maximum deflection of the beam. El is constant. 2a- A (b)
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- For the beam loaded as shown, use the method of superposition to determine the deflection of the beam at end A. Assume the following values: El = 2.8 x 104 kN-m² (constant for entire beam) L = 15 m w = 56 kN/m Answer: VA= i B W mm L C1. The figure shows Beam Diagram 3 provided by CISC Handbook of Steel Construction, where W=total applied load in kN. (1) using 4th-order differential equation to obtain the deflection equation y (i.e., Ar) for interval 0Sample Problem: Determine the reactions for the beam loaded as shown in the figure 15 KN/m below. 12 KN 6 KN /m 3m Rz R. 1.5 mHome Work: 1. Determine the maximum deflection d in a simply supported beam of length L carrying a uniformly distributed load of intensity w, applied over its entire length. 2. For the beam loaded as shown in the Figure, compute the moment of area of the M diagrams between the reactions about both the left and the right reaction. (Hint: Draw the moment diagram by parts from right to left). 500 N 2 m 1 m 1 m 400 N/m B R1 R2 Please solve according to the exporters of a typical solution. 1 M E*I 3. Moment Diagram by Parts but ds = pd0 M de M ds E*I 1 The construction of moment diagram by parts depends on two basic principles: 1) The resultant bending moment at any section caused by any load system is the algebraic sum of the bending moment at that section caused by each load acting separately. = de = %3D E*I ds but ds = dx (Flat curve) M Σ . de = -) M. = MR M = E * I 1 (M * dx EML,EMR : Sum of the moment caused by all the forces to the left and right section respectively. .. 0 = E * I 2)…Q4: Determine the maximum deflection and its location of the simply supported beam shown in the Figure. (E = 200 GPa) and (I= 65.0×105 mm²). 2 m 30 kN 15 kN +2m-201. The cantilever beam shown in the following figure is subjected to a load P or a deflection & at its free end. Two gages A and B are mounted at the same location on the top and bottom faces of the beam. Gage A is used to measure E., and gage B is used to measure E,. Assume that: E-30(10) psi, Poisson's ratio v-0.3 a) Determine theoretical values of E., b) Determine theoretical values of Strain gage A Strain gage B 14 in 12 in (μin/in) for a load of P-6 lbf. Ey (µin/in) for a deflection of 8-0.5 in. Por & 0.25Q2: For the uniform beam, determine the reactions at A and B, derive the equation of the deflection curve, and determine the slopes at A and B. A Y L B Wo XAlt Gr Ctri 2. The force P is acting onto the beam ABC through the rigid arm BD. Considering the effects of P at the point B and using Singularity Functions determine the deflection of the end point C. (EI is constant for ABC). D L/2 L/2 SHOT ON MI 6 MI DUAL CAMERAProblem 4 : Determine the reactions at supports A, C, and D of the beam shown in Figure. El - constant. 30 k B A 8ft (a) Actual beamCalculate the support reaction at A and B for the beam shown in the figure below. Take F= 570 N. F A B 3M 1M Ay By Reaction force at point B By= N. Reaction force at point A Ay N.5. A beam is loaded and supported as shown below. Use singularity functions to determine (a) The deflection at the midpoint of the beam. (b) The slope at C. Y A X -a- B ω a C a Dbeam, simply supported at its ends, carries a load which increases uniformly from 15kN/m at the left-hand end to 100 kN/m at the right-hand end. If the beam is 5m long, find the equation for the rate of loading and, using this, to determine the deflection of the beam at mid-span if E= 200GN/m² and I=600*10 m².SEE MORE QUESTIONS