It is obvious therefore to study the methods by which we can predict the deflection of members under lateral loads or transverse loads, since it is this form of loading which will generally produce the. The small deflection analysis of equal twospan continuous simply supported gfrp beams with cfrp flange stiffening is presented for the case of equal midspan point loads. Determine the slope and deflection at point b of the steel beam shown in fig. In this method, the area of the bending moment diagrams is utilized for computing the slope and or deflections at particular points along the. Beam deflection formula and equations for beams beam deflection equations are easy to apply and allow engineers to make simple and quick calculations for deflection. Essentially, it requires the same amount of conjugaye as the momentarea theorems to determine a beam s slope or deflection. Lecture 10 beams free download as powerpoint presentation. Solved gate questions on deflection of beams question 1.
Excessive deflection of a beam not only is visually disturbing but also may cause damage to other parts of the building. Hence, from basic calculus, the maximum deflection occurs at a rotation, 0. Deflection of beams study notes for civil engineering. This deflection is downward if the bending moment is positive to cause top fiber in compression in beam convention. A cantilever beam is 6 m long and has a point load of 20 kn at the free end. Jun 28, 2008 lecture series on strength of materials by prof. Aug 22, 2019 for instance, in the case of a simply supported beam with rigid supports, at x 0 and x l, the deflection y 0, and in locating the point of maximum deflection, we simply set the slope of the elastic curve y to zero. Mechanics of materials civl 3322 mech 3322 deflection of beams the elastic curve. If you have any doubts please refer to the jntu syllabus book. The maximum deflection occurs where the slope is zero. Lenguaje enoquiano pdf when the real beam is fixed supported, both the slope and displacement are zero. Stiffness method, which forms the basis of most computer software currentlyused for stt ltructural analilysis. Design of one way and two way slabs, design of staircases.
Example 3 draw the sfd and bmd for the beam acted upon by a clockwise couple at mid point solution. You can find most of the materialsnotes related to civil engineering. The angle subtended at the centre of the arc aob is. Previous years gate mcqs on deflection of beams 20012011.
Westergaard, deflection of beams by the conjugate beam method. Assakkaf spring 2003 enes 220 mechanics of materials department of civil and environmental engineering university of maryland, college park lecture 9. Aug 14, 2019 conjugate beam method nptel pdf haunched beams, and framed bents may be computed by a procedure. Another method of determining the slopes and deflections in beams is the areamoment method, which.
Calculating deflection by integration uniform load. The labor involved in solving problems of this type can be diminished by. May 26, 2015 solved gate questions on deflection of beams question 1. The slopedeflection method and a beam analysis code are implemented to analyze a large number of continuous beams of equal spans length. To prevent any attached brittle materials from cracking 2.
It does not involve the solution of many simultaneous equations. Deflection of beams study notes for mechanical engineering. At any distance x metres from the left end, the beam will have a. It is obvious therefore to study the methods by which we can predict the deflection of members under lateral loads or transverse loads, since it is this form of loading which will generally produce the greatest deflection of beams.
Ab is the original unloaded length of the beam and ab is the deflected position of ab when loaded. In this lesson, slopedeflection equations are derived considering the rotation of beam axis. Strength of materials is a fundamental subject needed primarily for the students of mechanical sciences. For prestressed beams the following aspects are important. Deflection of beam theory at a glance for ies, gate, psu 5. You can purchase classes at a very reasonable price. Jun 30, 2008 lecture series on strength of materials by prof. A segment is the portion of the beam between two nodes. General theory when a beam bends it takes up various shapes such as that illustrated in figure 1.
The deflection of a beam must often be limited in order to provide integrity and stability of a structure or machine, or. Calculate the slope and deflection at the free end. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. The method uses solutions of simple problems of in. In this chapter we learn how to determine the deflection of beams the maximum deflection under given load. Studying bending of beams, this is a standard case found in any textbook in solid mechanics or strength of materials. There are situations when parts of a beam bend upwards, and in these cases the signs of the normal stresses will be opposite to those shown in fig. Introduction slopedeflection method is the second of the two classical methods presented in this course. Structural analysisi notes pdf sai notes pdf notes. The ratio of end deflection to center deflection is also plotted in the figure. Bending of beams i bending of beams ii bending of beams iii bending of beam iv stresses in beams i stresses in beams ii stresses in beams. Sep 05, 2019 conjugate beam method nptel pdf haunched beams, and framed bents may be computed by a procedure. Beams of finite length x z ab a po general deflection solution sin cos sin cos 12 3 4 wx e c x c x e c x c x. Conjugate beam method nptel pdf haunched beams, and framed bents may be computed by a procedure.
Structural analysis 1 pdf notes sa 1 pdf notes file to download are listed below please check it note. Deflection method this method takes into account only the bending deformations. Slope deflection equations for prismatic beam columns using stability functions. However, the moments and shear forces shown in fig. A prismatic beam subjected to pure bending is bent into an arc of a circle in the elastic range,the curvature of the neutral surface expressed as.
The shape may be superimposed on an x y graph with the origin at the left end of the beam before it is loaded. Tbeams and doubly reinforced beams part i concrete design and analysis fall 2002 by dr. Beam deflection formulae beam type slope at free end deflection at any section in terms of x maximum deflection 1. In all the techniques an equation governing deflection at any point in the beam span is developed and expressed as a function loads, cross sectional and material properties of the beam. Jun 21, 2019 conjugate beam method nptel pdf haunched beams, and framed bents may be computed by a procedure. The position of the maximum deflection is found out by equating the slope equation zero. The first reinforced concrete design manual formerly titled aci design handbook was developed in accordance with the design provisions of 1963 aci 318 building code by aci. There are many methods to find out the slope and deflection at a section in a loaded beam. Foreword the reinforced concrete design manual sp1711 is intended to provide guidance and assistance to professionals engaged in the design of castinplace reinforced concrete structures. For this reason, building codes limit the maximum deflection of a beam to about 60 th of its spans.
Maximum deflection to find the maximum deflection we first need to find the location at which this occurs. Beam simply supported at ends concentrated load p at the center 2 1216 pl e i 2 2 2 3 px l l for 0yx x 12 4 2 ei 3 max pl 48 e i x 7. Deflection is defined as the vertical displacement of a point on a loaded beam. A simply supported prismatic beam ab carries a uniformly distributed load of intensity w.
Cantilever beam concentrated load p at any point 2 pa 2 e i lei 2 3for0 px yax xa 6 ei 2. Design of members subjected to combined bending, torsion and axial loading. If youre unsure about what deflection actually is, click here for a deflection definition below is a concise beam deflection table that shows how to calculate the maximum. Calculate a rotation at some point, say support a, using mohr ii say. Deflection equations skyciv cloud structural analysis. Spend time on studying, not for searching material to study. Moduleiii design of short and long columns with axial and eccentric loading, design of isolated column footing.
Deflection equations skyciv cloud structural analysis software. To prevent any attached brittle materials from cracking 2 beam deflection by integration. Member fixed end actions for uniform and concentrated load. For instance, in the case of a simply supported beam with rigid supports, at x 0 and x l, the deflection y 0, and in locating the point of maximum deflection, we simply set the slope of the elastic curve y to zero. The area moment of inertia of a square of size 1 unit about its diagonal is a b 14 c 112 d 16 gateme2001 hint hint 1. Structural analysis iii the moment area method mohrs. In statically indeterminate structures, the beam axis rotates due to. For full lectures, chapter wise log on to our website. Lecture 12 deflection in beams linkedin slideshare. Beam simply supported at ends concentrated load p at any point 22 1 pb l b. Cantilever beam concentrated load p at the free end 2 pl 2 e i nm 2 3 px ylx 6 ei 24 3 max pl 3 e i max 2. Deflection method in displacement method,theunknown displacements are determined first by solving the structures equilibrium equations. Draw fbd of the beam and calculate the support reactions draw the sfd and the bmd starting from any one end c l c v l c m 2 c 2 c me101 division iii kaustubh dasgupta 8.
In r and r15,8units of r09 syllabus are combined into 5units in r and r15 syllabus. As the engineering design of different components, structures etc. A number of analytical methods are available for determining the deflections of beams. Beam deflection formulas beam type slope at ends deflection at any section in terms of x maximum and center deflection 6. The goal of this site is presently to help the undergraduates pursuing b.
Nptel provides elearning through online web and video courses various streams. Used by engineers for analysis of small structures. Scan the beam and identify the number of a segments and b kinematic unknowns. This is covered in text books of structural analysis. These notes are according to the r09 syllabus book of jntu. Application of limit state method to rectangular beams for flexure, shear, bond and torsion.
The ratio of center deflection changes with the length of the beam. Beams of various span numbers and loading distribution are. Discontinuous singularity functions for beam deflections the iiintegration methdhod becomes extremely tedious and time. Ei 1 m from calculus, the curvature of the plane curve shown is given by.
1080 600 238 484 1019 477 1232 1018 924 1534 395 1536 1173 1553 640 315 1481 309 1052 648 304 1143 1143 970 220 510 942 1147 553 218 957 1469 545 616 611 599 593 1438 235 674 1440 879 478 156 1031 561 1466 511