The boundary-value problem for a cantilevered beam can be written as
Assume
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Introduction To Finite Element Analysis And Design
Additional Engineering Textbook Solutions
Manufacturing Engineering & Technology
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Applied Statics and Strength of Materials (6th Edition)
Statics and Mechanics of Materials (5th Edition)
Engineering Mechanics: Dynamics (14th Edition)
Degarmo's Materials And Processes In Manufacturing
- 2. Draw shear force and bending moment diagrams for the beam shown in figure. 50 kN/m 20 kN/m 2 m 2 m - 2 m Ro Hello sir, please the same source as the question solution. 3. Relation between load, shear and moment: The free body diagram wdx :- %3! W (N/m) 严 of segment of this beam of length (dx) is shown M+4M but wdx is the summation of area between (x, and x2) in figure (2). V+av ..V, -V, = AV = (area) nad RI %3! similarly M2 (1) (2) ( dM = Vdx EF, =0= V +wdx-(V+dV)%3D0 w ------- Intensity of load (N/m) . dV =wdx M1 M, - M, = AM = (area ) hm %3! dx M, =0= M+Vdx + (wdx)-(M + dM) =0 shear AP . W =- (dr)? dx (slope of shear diagram) Where: :ero 2 .. dM Vdx dM :.V = dx (slope of moment diagram) for (dV = wdx ) we can integratingarrow_forwardD 40.0 cg 30.0⁰ H 2.0 m draw the free body diagram. draw the vector starting at the black dogs. The location and orientation matter. A uniform, 3.0 m, 1250 kg beam is hinged to a wall and supported by a thin cable attached 2.0 m from the free end of the beam (Figure 1). The beam is supported at an angle of 30.0° above the horizontal.arrow_forwardA fixed-end beam of length L is loaded by a distributed load in the form of a cosine curve with maximum intensity qo at A. a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve b) Evaluate the rotation at L/3 for L=2 m and qo= 20 kN/m |y 9o cos 2L X- A Вarrow_forward
- Consider the beam in the picture below: 7kN/m 5kN/m P N/m Section 1 Section 2 Section 3 - L/3 L/3 L/3 Take P = the last four digits of your student number in N/m. If P<250 N/m then take P = 30OON/m instead. Take L = the third digit of your student number, reading left to reight. If this value is zero then take L = 2 Assume: The reaction at the Pin = Vnin 47000L+9PL )N %3D 54 The reaction at the Roller = Vroller = 61000L+9PL 54 N and that both reactions act vertically upwards. a) Find an expression for the internal moment for Section 1. Show all working and any relevant free body diagrams. b) What is the maximum magnitude of the internal moment for Section 1? Mark sure you prove that the value you calculate is the maximum. c) Find an expression for the internal moment for Section 2. Show all working and any relevant free body diagrams. d) What is the maximum magnitude of the internal moment for Section 2? Mark sure you prove that the value you calculate is the maximum. e) Find an…arrow_forwardy التاناتي The boundary conditions are Р L The strong form of governing equation for a simply supported beam under a distributed load p, shown in the figure above, is as follows d²v M(x) dx² X 0 EI where v is the deflection in y direction, E is Young's modulus, I is the second moment of inertia, M(x) is the internal bending moment and is given by px(L-x) M(x) = 2 v(0) = 0 v(L)=0arrow_forwardDetermine the maximum compressive bending stress (o max.comp.x=2.8) for the beam section at distance 2.8 m from A, for the beam loaded in Figure 5.1la1(b), in N/mm2. The cross section of the beam is shown in Figure 5.1a1(a). Given D = 120 mm, t = 15 mm, location of centroid of the cross section = 62.1 mm from x-axis, second moment of area with respect to its centroidal x-axis (Iy) = 7.08 x 106 mm“, a = 0.9 m, b = 0.9 m, and P1 = 20 kN. (Note: Use negative sign "-" to denote compressive stresses) t; D Figure 5.1a1(a) P, kN A В D a m b m 3 m Figure 5.1a1(b)arrow_forward
- A wooden beam is loaded by a concentrated load P = 1000 N and supported by boundary conditions as shown in Figure Q5(a). The cross-section of the beam is shown in Figure Q5(b). Given that LAB = 1600 mm, LBc = 3400 mm, Bô=10 mm, B₁ = 20 mm, and H = 230 mm, ho=150 mm, h₁ =40 mm, determine the following quantities below:arrow_forwardConsider a horizontal, uniform beam that extends from x = 0 m to x = 2.5 m. The beam is supported at each end by two strings which exert forces directly upward. There is a downward force per length on the beam given by dF/dx = 488 x (2.5 - x) (N/m), which includes any weight force on the beam. Calculate the tension in the rope attached to the right end of the beam. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forwardConsider the following values in the given beam above: L1=6m L2 = 2 m L3 = 4 m L4=3m L5=2 m L6=1m W1 = 90 kN/m W2 = 30 kN/m P = 50 kN M = 60 kN-m Point E is an internal hinge W1 B L2 L3 2 m E W2 L5 L6 Harrow_forward
- Consider a beam supported by a pin and at A and roller at B subjected to uniform distributed load w=300 N/m. If the expression of elastic curve for coordinates x1 and x2 are written as follow: V₁00=1/El [ax³+ Clx+ C2] V₂ (x)=1/El (bx4 + C3x + C4] Determine the reactions at the supports, the expressions of internal bending moments and the constants C1, C2, C3 and C4. By = M1 => M2- CL= (2- 150 downward 100 downward 100 upward 250 upward 500 downward 450 upward -50x -150 x^2 -150x -50 x -50 50 25 16.67 8.33 0 1m 100-80 50 -50 x^2 -100 x^2 -16,67 -68.7 -87.5 W 1marrow_forwardQ6/Draw the shear force and bending moment diagram of simple supported beam AB as shown in figure 5. 150N C 300N B Figure 5 Im 2marrow_forwardThe dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C. What is the reaction force at A? Let a positive reaction force be to the right.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY