Cantilever deflection of beams problems with solutions pdf download. Calculate the slope and deflection at the free end.

Cantilever deflection of beams problems with solutions pdf download. With the cantilever beam under a point load at the tip in.

Cantilever deflection of beams problems with solutions pdf download. , a set of nonlinear differential equations for the analysis of the single cantilever beam was proposed, and the applicability of the model to the cantilever beam deflection problem was demonstrated. M. 00327 and -13 mm). 2 and 3, gives the following information (taking the origin of the coordinate system as node 1) DOI Take the deflection at the centre of beam using dial gauge. \(EI\) = constant. Draw the SFD and BMD for the beam acted upon by a clockwise couple at mid point. View PDF. Use E = 1. Chen [36] proposed an integral approach by using the moment integral treatment, unlike the elliptical integrals, which can be applied to problems of complex force load and variable beam properties such as Jun 1, 2008 · When the boundary conditions are applied correctly, the optimum mesh or grid for solution of the problem is always uniform. Key words: Cantilever beam, FEM, Mild Steel. V. The document discusses various methods for analyzing beam deflection and deformation under loading, including: 1) Deriving the differential equation for the elastic curve of a beam and applying boundary conditions to determine the curve and maximum deflection. The real and virtual systems are shown in Figure 8. 2) using the Kras- noselskii fixed point theorem [6, Theorems 4. 47 mm. 2) is much more interesting. We learned Direct Stiffness Method in Chapter 2. Take EI=7×10 4 kNm2. Determine V and M relations for the beam. the hub which is assumed to be a rigid disc with radiu s Apr 1, 2013 · The paper [8] proposed the direct numerical method for the large deflection problem of a non-uniform straight cantilever under a tip-concentrated follower force. It introduces the concepts of bending moment (M), modulus of elasticity (E), and moment of inertia (I) in determining curvature and deflection. Cantilever beam. Macaulay’s Method is a means to find the equation that describes the deflected shape of a beam. 10kN 45o 1m 3m A x A y B y C A B θ x y FAB AkN MB BkN FA A kN Overallequilibrium y yy y A y y x x x 0 10sin45 1. 4: Apply the same procedure for another beam with different dimensions. used the homotopy analysis method (HAM) for this problem with approximate solutions in power ¥ A Problem 637. Solve when number of equations = number of unknowns. 2 To determine the modulus of elasticity of the beam and what the material the beam is made of using beam deflection theory. Find the height h if the maximum deflection is not to exceed 10 mm. 4 KN-m ; MFBA = +3. The results presented by him for uniform cantilever beam show Module 5. With the cantilever beam under a point load at the tip in. A beam is a structural element that is capable of withstanding load primarily by resisting bending. The beam is subjected to a compressive load P , as shown in the gure. Previously an approximate solution had been obtained by Gross und Jan 4, 2011 · Jan 4, 2011 • Download as PPT, PDF •. 4a. 10a is subjected to a concentrated moment at its free end. Before Macaulay’s paper of 1919, the equation for the deflection of beams could not be found in closed form. Calculated example 8A: Deflection of cantilever beam For the cantilever beam shown in Figure 8-2, determine the equation of the elastic curve by direct integration. \(Fig. . The cantilever beam shown in Fig. Solution Based on the free body diagram shown in Figure 8-2, the solution to the moment and vertical force equilibrium equations is obtained as R A =P and M A =-PL. For the cantilever of Problem 2, find the maximum slope and deflection. The left side of the cantilever beam is fixed while there is a point load of segment AB of our cantilever beam, Equation 3 turns into Equation 1. State the boundary conditions of a deflected beam Determine the deflections and slopes of elastic curves of simply supported beams and cantilever beams. Nov 8, 2021 · The purpose of this paper is to prove the existence of solutions (small deflections) of the cantilever beam boundary value problem (6) under the conditions (7)-(13). This interesting problem has A Cantilever beam is one, which is anchored at only end. θ = PL2 2EI θ = P L 2 2 E I. u(x) = (l x) (5. Write down the load function p(x) in each segment. Fig. 1), (1. – Each statically indeterminate beam problem has its own peculiarities as to its method of solution. Exercise 4. Split the beam into segments. anything nice Jul 2, 2022 · This is widely known as the elastica problem, which has been extensively stud-ied [32–34]. Problem Description This is a simple, structural analysis of a cantilever beam. 1 General. To determine the reaction at support A of the beam, apply the equation of equilibrium, as follows: + ↶ ∑ M A = 0 M A − 4 ( 6) ( 9 Apr 3, 2024 · Get Deflection of Beam Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. 3. From the figure above, the deflection at B denoted as δB is equal to the deviation of B from a tangent line through A denoted as t B/A. spBeam is widely used for analysis, design and investigation of beams, and one-way slab systems (including standard and wide module joist systems) per latest American (ACI 318-14) and Canadian (CSA A23. V Potential of. is a square). The case in which the nonlinear term is retained in Eq. 2, April 2020 357 DERIVATION AND OPTIMIZATION OF DEFLECTION EQUATIONS FOR TAPERED Correlation between ANN & FEM models for 58. Force-Displacement (Stress-Strain) Relations. This document discusses determining the deflection of beams under load. They can also be used in bridges and other structures to Example - Cantilever Beam with Single Load at the End, Metric Units. 2)mustbe zero. Free Body Diagram. This equation gives the deflection at all values of x and produces a maximum value at the tip of the cantilever, therefore to find a maximum deflection substitute x = 0, Maximum deflection = y max = − WL3 3 EI (6. 175 Lower limit 0. It is customary to call A'B' the curved axis of the beam as the elastic line or deflection curve. A direct method for the large deflection problem of a non-uniform spring-hinged cantilever beam under a tip follower force was proposed by Shvartsman [28]. Displacement Compatibility IV. P-641, what will cause zero deflection at A? Solution 641. As load is applied on a beam, it deflects. Equilibrium of Forces (and Moments) III. I. Solution 637. Wang et al. In the notes of lecture 5 the solution of this problem was outlined, but not completed, Complete the derivation by calculating all four integration constants. Download these Free Deflection of Beam MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. Elastic curve. Assume tensile forces act on all the members. The result gives an affirmative answer to the question of existence of solutions of -, i. Problem 636. Problem Specification. 1 Problem 9. (note lengths L,a,b) 3: Change the arrangement of the apparatus for the cantilever beam, load it intermediately. Limited to simple elements such as 1D bars. the asymptotic solutions of larger numbers of terms. Select appropriate support, symmetry, and continuity conditions to solve for constants of integration. 1The exact expression for curvature is d ds = d2v=dx2. The classical problem of the deflection of a cantilever beam of linear elastic material, under the action of an external vertical concentrated load at the free end, is analysed. Nov 8, 2021 · This interesting problem has not been studied in research. It is clamped on the left side and has a. INFLUENCE LINE Reference: Structural Analysis Third Edition (2005) By Aslam Kassimali fDEFINITION An influence line is a graph of a response function of a structure as a function of the position of a downward unit load moving across the structure fINFLUENCE LINES FOR BEAMS AND FRAMES BY EQUILIBRIUM METHOD Influence Apr 9, 2011 · Deflection of beams. To determine the slope at free end & also deflection at free end I = 1 Apr 16, 2021 · A cantilever beam shown in Figure 7. propped cantilever beam shown in Figure 1. beam. 4e, respectively. There are four unknown reactions in the beam: the reactive moment, a vertical and horizontal reaction at the fixed end, and another vertical reaction at the prop at point B. Nov 1, 2006 · at least one positive solution to the nonlinear boundary-value problem (1. A simple support for the real beam remains simple support for the conjugate beam. (a) Determine the deflection of a coil spring under the influence of an axial force F, including the contribution of bending, direct shear, and torsional shear effects. 1 Determine the equations of the slope and deflection curve for a beam shown in figure P9. 3 To verify the principle of superposition and Maxwell’s Reciprocity Theorem. The unsupported end is known as the cantilever, and it extends beyond the support point. 8 Solution to Problem 648 _ Deflection of Cantilever Beams _ Strength of Materials Review - Free download as PDF File (. 12, 4. J. P-637, determine the deflection 6 ft from the wall. 1 depicts a schematic view of a cantilever beam subjected to a combined tip point loading, including a general moment M 0 and a general force f 0 with an angle ϕ. Tags: cantilever beam. (5. δ = PL3 3EI δ = P L 3 3 E I. 36 N/mm load (zoomed in) Conclusion The maximum deflection of a cantilever beam under distributed load was predicted using Artificial Neural Network. 5. Christian Otto Mohr. The beam has constant EI for both the spans. P-644. Jan 1, 2010 · axis of the wing and both free ends beams along vertica l The cantilever beam is shown in Fig. By using the moment integral treatment, this approach can be applied to problems of complex load and May 1, 2021 · Abstract and Figures. pdf), Text File (. 10 Upper limit 0. Sivakumar Introduction The axis of a beam deflects from its initial position under action of applied forces. Deflection of a Cantilever Beam. 5m from the free end. 1. Cantilever Beam – Uniformly distributed load (N/m) 3 6 l E I 2 22 64 x yxllx EI 4 max 8 l E 4. 6 Determine the deflection at B for the beam using conjugate beam method. 4c, and Figure 8. Aug 18, 2023 · intuitive for the evaluation of solutio ns in comparison with. Solution: Draw FBD of the beam and Calculate the support reactions. SOLUTIONS. Compute the value of δ at the concentrated load in Prob. The 4slope of beam is obtained by direct integration of Jan 1, 2022 · With this method, the deflection of the cantilever beam can be precisely estimated regardless of the load conditions and deflection modes. 2) Using the method of superposition to Problem 641. Table 2: Design values for the tapered cantilever beam with constant height Design Variable W1 (m) W2 (m) Start value 0. Consider a beam AB which is initially straight and horizontal when unloaded. If there are no distributed loads in a segment, p(x) = 0 3. 4a, Figure 8. Integrate Moment-displacement differential equation. 20 Deflection by Superposition ENES 220 ©Assakkaf General Procedure of Superposition – It is evident from the last results that the slope or deflection of a beam is the sum of the slopes or deflections produced by the individual loads. The deflection can be observed and measured directly. FBD of the entire beam (do not need to enforce equilibrium) 2. Solution steps: (1) The coordinate x is now taken from the left end. The beam differential equation is integrated twice – deflection of beam at any c/s. 1 Solution The differential equation of the deflection curve of a beam is as below: d2y dx 2 y Mb EI EIy M b where y – is deflection of the beam neutral axis E – is Young’s modulus I – is moment of inertia of the beam cross-section respect to neutral Oct 4, 2022 · Problem 5. 30 0. Click here to show or hide the solution. 5a. 50 0. Abstract. demonstrated by applying it to a cantilever beam, s ubjected to. Rotation and Deflection for Common Loadings. By integrating over the physical domain with the Galerkin m ethod and approximate solutions Problem 27 -Solution Consider the FBD of the truss as shown to get the unknown reactions at A and B as shown. Support reactions. 11). txt) or read online for free. Also, sketch the deflected shape of the beam. Figure 1, the Apr 24, 2012 · In this paper large deflection and rotation of a nonlinear Bernoulli-Euler beam with variable flexural rigidity and subjected to a static co-planar follower loading is studied. To determine the unknown reactions in the beam, one more equation must be added to the three equations of equilibrium. A cantilever beam is 6 m long and has a point load of 20 kN at the free end. Problem 644. 8 Determine the expression for the slope and deflection of the free end of the cantilever beam shown in the Figure T4. 1 To observe, evaluate and report on the load-deflection relationship of a simply supported beam and a cantilever beam. ∑MA = 0 RA = 60 N ∑MB = 0 RB = 60 N. M/ Aug 24, 2023 · Using the virtual work method, determine the deflection and the slope at a point B of the cantilever beam shown in Figure 8. xstresses(showninFig. 17 ENES 220 ©Assakkaf Sep 15, 2012 · Large deflection of a cantilever beam subjected to a tip-concentrated load is governed by a non-linear differential equation. 3. – But there are some general rules and ideas that are common to the solution of most types of beam problems. The asymptotic solutions with the terms satisfying the boundary conditions are Solution to Problem 638 _ Deflection of Cantilever Beams _ Strength of Materials Review - Free download as PDF File (. Apr 16, 2021 · Using the method of singularity function, determine the equation of the elastic curve of the beam, the slope at the free end, and the deflection at the free end. The EI diagram for the cantilever beam is shown below. Cantilever Beam – Concentrated load P at any point 2 Pa 2 E I lEI 2 3for0 Px yax xa 6 EI 2 3for Pa yxaaxl 6 EI 2 3 Pa 6 la EI 3. 14]. Draw the SFD and BMD for the beam. These are the same as calculated in the previous problem: MFAB = -2. A realistic model of a cantilever which includes a support region of finite stiffness and the INTRODUCTION. 4 . 1. 4. Sivakumar Strength of Materials Deflection of beams Introduction Deflection of Beams (Solution Method by Direct Integration) Moment - Area Method for finding Beam Deflections Indian Institute of Technology Madras Strength of Materials Prof. Interlayer slip, horizontal Solution to Problem 644 | Deflection of Cantilever Beams. 3 Con j u ga t e Be a m M e t h od The conj ugat e beam m et hod is an ext rem ely versat ile m et hod for com put at ion of deflect ions in beam s. downwards. and the solution is. Problem –2: A steel cantilever beam of 6m long carries 2 point loads 15KN at the free end and 25KN at the distance of 2. The validation and ca pability characteristics was. Apr 17, 2024 · Choose formula: PL³/ (48EI). Consider the beam in the figure below. Point A is chosen at the fixed end where θ A = 0 and hence the tangent to the elastic curve is horizontal, and point B, to the right of A, at the free end. The effects of taper ratio, inclined end load angle and material property gradient on large deflection of the beam are evaluated. Barten, "On the Deflection of a Cantilever Beam," Quarterly of Applied Math. II. Integrate load-deflection equation four times →equations for V(x), M(x), v Oct 9, 2006 · The classical problem of the deflection of a cantilever beam of linear elastic material, under the action of an external vertical concentrated load at the free end, is analysed. 3 4 6 meters ( cross - section. The maximum moment at the fixed end of a UB 305 x 127 x 42 beam steel flange cantilever beam 5000 mm long, with moment of inertia 8196 cm 4 (81960000 mm 4), modulus of elasticity 200 GPa (200000 N/mm 2) and with a single load 3000 N at the end can be calculated as. Solution to Problem 640 | Deflection of Cantilever Beams. T4. , 2, 168-171 (1944). Aug 1, 2020 · Argyris and Symeonidis [1] studied static nonlinear analysis of a cantilever beam subjected to follower loads by the finite element method in order to find the critical flutter loads. 3 4 6 meters and height of 0. [1+ (dv=dx)2]3=2. Calculate the slope and deflection at the free end. The constants E and I are, respectively, Young's modulus and the moment of inertia of the beam's material and uniform cross section; s and θ are, respectively, the arc length and the angular deflection of the beam; and x and y A Cantilever beam is one, which is anchored at only end. Cantilever beams are often used in construction to support balconies, roofs, and other overhangs. The method is based on approximating the angle of rotation of the deflected beam axis by an Nth order polynomial. LECTURE 19. This is because the tangent line through A lies with the neutral axis of the beam. May 3, 2002 · Abstract. Determine the maximum deflection for the beam loaded as shown in Fig. Using the moment-area method, determine the slope at the free end of the beam and the deflection at the free end of the beam. We now turn our attention to the solution of the beam de ection, Eq. Download Free PDF. (Answers 0. – Once the slopes or deflections The outputs of finite element simulation are used to investigate the effect of point load on product integrity and mechanical properties. In the formulation of the problem, the nonlinear Sep 27, 2011 · The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam. q A B l Fig. The above procedure completed the full calculation of the deflection of a cantilever beam under a point load at the free end including the movement of the free end. 7 Determine the mid-span deflection for the beam using conjugate beam method. 1 Introduction When a structure is placed under load it will bend, deflect or displace. This will be dealt with in the section on moderately large de ection of beams. 4 × 10⁵ × 72 × 10⁶) = 3. 10 0. Thiscanbeexpressedas. 1 This problem was considered by H. Nov 24, 2023 · A cantilever beam is a structural element that extends horizontally and is supported on only one end. Using r = 1 mm and R = 10 mm, compute the relative magnitudes of the three contributions. A cantilever beam is 5 m long and has a point load of 50 kN at the free end. The governing equation of this problem is solved analytically for the first Cantilever Beam Analysis and Design –spBeam Software. Since it is hard to find exact or closed-form solutions for this non-linear problem, this paper investigates the aforementioned problem via the differential transformation method (DTM) and the variational iteration method (VIM), which are well-known approximate A unit-width cantilever beam with a point load B. Dec 1, 2010 · Navaee and Elling [9] have studied equilibrium configurations of a cantilever beam subjected to an end load with constant angle of inclination. Notice that the real Mar 1, 2010 · In cases where the cantilever beams are subjected to the follower force, an exact closed-formed solution has been developed using elliptic integrals for large deflection analysis of an elastic the shortening of the moment arm become the major contribution to the solution of * Received April 6, 1945. Write down the load-deflection equation for each segment: 4. Enter values: 45 × 10³ × (4 × 10³)³/ (48 × 2. Dec 18, 2018 · Triangular (LST) elements for deflection analysis on cantilever. Abstract: The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach. Thus EI is an index of the bending (flexural) strength of an element – called Flexural Rigidity of the element. 6) The negative sign indicates that deflection is in the negative y direction, i. 8. Potential energy: Sum of strain energy and potential of applied loads. Use E = 10 GPa. The flexural stiffness is 110 MNm2. Nov 30, 2021 · The following conclusions are drawn: (1) In light of the large deflection nonlinear differential equations proposed by Duan et al. For the beam loaded as shown in Fig. 2. FEM Solution of Deflection on a Cantilever Beam For the development of the model, the following major steps were employed: Step 1: Idealization and discretization The idealization, shown in Fig. 39, No. Maximum Moment. length of 4 meters, width of 0. Procedure for Statically Indeterminate Problems. BEAMS: STATICALLY INDETERMINATE (9. 10\). Solution 636. Solution. M = −PL M = − P L. , the existence of small deflections of general types of perturbed cantilever beams under conditions -, including the simple cantilever beam problem when . Solution (\(M/EI\)) diagram. The original non-linear boundary value problem transforms into the initial value problem. Statically Indeterminate Transversely Loaded Beams LECTURE 18. In this paper, Euler–Bernoulli’s equation is adapted along with R. Deflection Equation ( y y is positive downward) Dec 9, 2019 · The problem of large deflection of a composite cantilever beam under a vertical concentrated load at free end is studied in this paper. Structure is in equilibrium when the potential energy is minimum. The Timoshenko and Goodier [1] solution for a cantilever beam is therefore unsuitable as a test problem for adaptive procedures. It is assumed that the angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation. Fourth order Runge–Kutta method was used for solution of the initial value problem. For the cantilever beam shown in Fig. From this equation, any deflection of interest can be found. The length of a conjugate beam is always equal to the length of the actual beam. A fixed end for the real beam becomes free end for the conjugate beam. point force of 8 k N acting downward on the right end of the beam. Cantilever Beam – Uniformly varying load: Maximum intensity o 3 o 24 l E I 2 32 23 o 10 10 5 120 x yllxlxx 4 o Problem –1: Determine the deflection of a given beam at the point loads. BEAMS: DEFORMATION BY SUPERPOSITION (9. The governing differential equation along with the beams Mar 1, 2013 · Fig. This beam deflection calculator will help you determine the maximum beam deflection of simply-supported or cantilever beams subjected to simple load configurations. Problem 640. Apr 1, 2010 · The bending problem of a cantilever beam is schematically defined in Fig. The maximum deflection can be obtained by solving the second order differential equation that governs the Jan 1, 2021 · A new integral approach is proposed to solve the large deflection cantilever beam problems. Maximum deflection of a cantilever beam was initially calculated through FE simulation. Calculate desired deflection (v) and slopes (θ) Engr. Kenneth Alambra and Nicholas Swanson. Real and virtual systems. 7. We seek to nd conditions under T4. Now that we know the basis for the theorem, let’s use it to calculate the free end rotation at the of the beam. This gives ˇdv=dxwhen the squared derivative in the denominator is small compared to 1. 2: Bifurcation of equilibrium in a compressed cantilever beam Consider a cantilever beam of length L made of a material with Young's modulus E and whose uniform cross section has a moment of inertia with respect to the x 2 axis I22. Results were then categorized to train artificial neural networks. Case 1: Concentrated load at the free end of cantilever beam. May 1, 2011 · For the large deflection problem of beams, the new solution for the rotation angle is more approachable to the engineering designers than the implicit exact solution by the Eu-ler-Bernoulli law. (a) Fixed end moments. e. 18 Solution: Draw FBD and find out the. Aug 27, 2018 · The solution methodologies for nonlinear differential equations play a significant role in the area of theoretical mechanics, in particular large deflection of beams. Slope at end. Maximum deflection. There are different types of beams, like cantilever beam, simply supported beam and in that there will be different types of cross-sections, like rectangular, circular etc. 5 × 10 6 psi and I = 40 in 4. 1 attached t o direction of the axis. S. The deflection at the free end is 3 mm downwards. Problem 5-5: Continuity Condition. Using the slope deflection method, compute the end moments and plot the bending moment diagram. 50 Figure 2: The optimisation tool dialogue box Nigerian Journal of Technology, Vol. P-636 has a rectangular cross-section 50 mm wide by h mm high. Under the assumption that the material of beam remains linearly elastic, the relationship of bending moment and beam deformation reads ([1]) (1) d θ ds = M (s) EI where θ is the angle of rotation of the deflection curve, s is the distance measured along the beam, M is the bending moment, E is the module of elasticity Figure 9. Is the deflection upward downward? Sep 7, 2022 · T he Approximate Solutions of Large Deflection of a Cantilever Beam. 639. If under the action of loads the beam deflect to a position A'B' under load or infact we say that the axis of the beam bends to a shape A'B'. The elastica of nonprismatic cantilever beams with rectangular cross-sections that are subjected to combined loading was studied by Lee [35]. 8) Slide No. Da Silva method for solving the problem of large deflection on multilayered cantilever beams with interlayer slip analytically. 6 KN-m. Solve the problem of a simply-simply supported beam loaded by a point force acting at eh symmetry plane, but at a distance a from the left support. support reactions using equilibrium equations. The deflection of beam for UDL is obtained by direct double integration of moment at section “x” from fixed end as in equation (12). This theorem has recently been applied A Cantilever beam is one, which is anchored at only end. M odu le 4 : D e fle ct ion of St r u ct u r e s Le ct u r e 2 : Con j u ga t e Be a m M e t h od Obj e ct ive s I n t his course you will learn t he following Com put at ion of deflect ion using conj ugat e beam m et hod. P 9. Prof. 2: Change the position of the load, and measure the deflections between AC and BC. Deflection by Integration. Answer the Question! – Typically calculate desired internal. The deflection will depend on the following factors: 1. 4. Take I = 64x10-4 mm4 & its Young’s modulusN/mm (E). N. This kind of substitution can transform the basic equation, an integral differential equation into nonlinear algebraic ones, thus simplify Nov 1, 2005 · A robust and stable numerical scheme for the solution of very large deflection problem for prismatic and non-prismatic slender cantilever beams is presented in this paper. 3-14) codes. 7 – 9. E = 29 × 10 3 ksi, I = 600 in 4. a point Procedure for Analysis. Recently, Shavrtsman [10] has presented a direct method for the large deflection problem of a cantilever beam under a tip follower force. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam. spBeam can be used for new designs or investigation of existing structural Aug 1, 2018 · In this paper, Euler–Bernoulli’s equation is adapted along with R. M max The tangential deviation in this case is equal to the deflection of the beam as shown below. Under a Point Load. In this work, the static deflection of internal stepped cantilever beams with two steps was selected to be investigated by using Finite Element Method (FEM), Classical A comparison of the approximation and exact solution of horizontal length at the end of the beam. Deflection by Superposition •If stress-strain behaviour of the beam material remains linear elastic, principle of superposition applies •Problem can be broken down into simple cases for which solutions may be easily found, or obtained from data handbooks (see Appendix C of the textbook) Problem 9. We Apr 1, 2006 · The large deflection problem of cantilever beams was studied by means of the biparametric perturbation method and the first order derivative substitution from pseudolinear analysis approach. The beam has a. 21) EA. 5) Slide No. Draw a FBD including reaction forces. Consider the equilibrium at each hinge to find the force in the members. we will learn Energy Method to build beam finite element. uu wg kp jw lb ik ed mj zg ls