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This laboratory work sheet guides students through experiments focused on beam shear and bending moments. It includes theoretical backgrounds, objectives, and procedures for measuring shear force and bending moments in beams under varying loads, using specified apparatus. Results derived from the experiments aim to be compared with theoretical expectations to assess the accuracy of the methodologies employed.
The shear capacity of the concrete beams having stirrups is assumed as the sum of individual contributions of both the concrete and shear reinforcement. Different international building codes have suggested empirical relations for both of these contributions. In this research seventy beams with five values of longitudinal reinforcement and seven values of shear span to depth (a/d) ratios were tested in two sets of thirty five beams each, without and with shear reinforcement to study the contribution of the stirrups in resisting the shear. The beams were tested under the concentrated load at the mid span. The test results were analyzed for the contribution of stirrups, the effect of longitudinal steel and shear span to depth a/d ratios. It has been shown by the results that the assumption of summing the individual contribution of steel and concrete for the shear strength of reinforced beams is not proved.
2021
Figure shows a simple beam, one of the widely used statically determinate beams loaded with a central point load W.
Periodica Polytechnica-civil Engineering, 2023
The shear behavior is one of the most mysterious physical phenomena of an RC (reinforced concrete) beam. Many shear-transfer actions (such as dowel action, cantilever action, aggregate interlock, tension softening, etc.) affect it. Still, there is no scientific agreement on the number and the role of these phenomena. The paper investigates the historical development of these shear-transfer actions and the calculation models made from them through the glass of experimental research in the last one and half centuries in Hungary, in the context of the current international state of the art. This historical approach gives us an understanding of how the researchers and engineers of the past tried to understand the structure, and it leads us to accept that we are also on the way to understanding the shear behavior. However, the perfect model and understanding are far away from now. But are we on the right way?
Journal of Al-Azhar University Engineering Sector
Existing structures are subjected to increasing loads. They were often designed using Allowable Stress Design method (ASD). In old industrial buildings, beam dimensions were selected compact by using either rolled steel sections, or built up profiles. A direct design method is presented to strengthen such continuous beam panels above their plastic limit at different locations. Shear yield strain is crucial in the analysis, which is considered by using a numerical solution, and then simplified formulae are presented. The strengthening is based on attaching steel plates at the suitable locations. The position of each plate and its reasonable extension is determined. Material consumption and welding energy are kept as low as possible. Results are compared with previous tests and numerical values. Excessive strengthening is avoided. The proposed method could be applied on beams with other dimensions and/or conditions. The required precautions and restrictions are given.
Problem 1.2-2 Segments AB and BCD of beam ABCD are pin connected at x ϭ 4 m. The beam is supported by a sliding support at A and roller supports at C and D (see . A triangularly distributed load with peak intensity of 80 N/m acts on BC. A concentrated moment is applied at joint B. (a) Find reactions at supports A, C, and D. (b) Find internal stress resultants N, V, and M at x ϭ 5 m. (c) Repeat parts (a) and (b) for the case of the roller support at C replaced by a linear spring of stiffness k y ϭ 200 kN/m.
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1) To determine the bending moment and shear force on the beam.
Shear Stress in Beams: When a beam is subjected to nonuniform bending, both bending moments, M, and shear forces, V, act on the cross section. The normal stresses, σ x , associated with the bending moments are obtained from the flexure formula. We will now consider the distribution of shear stresses, τ, associated with the shear force, V. Let us begin by examining a beam of rectangular cross section. We can reasonably assume that the shear stresses τ act parallel to the shear force V. Let us also assume that the distribution of shear stresses is uniform across the width of the beam. Shear stresses on one side of an element are accompanied by shear stresses of equal magnitude acting on perpendicular faces of an element. Thus, there will be horizontal shear stresses between horizontal layers (fibers) of the beam, as well as, transverse shear stresses on the vertical cross section. At any point within the beam these complementary shear stresses are equal in magnitude. The existence of horizontal shear stresses in a beam can be demonstrated as follows. A single bar of depth 2h is much stiffer that two separate bars each of depth h.
Engineering Proceedings, 2025
The beam-column connection is an important element in frame construction. Despite numerous studies, there is still no uniform procedure for shear force design across countries. We continue to witness serious problems and even collapse of buildings under seismic activity caused by failures in the beam-column connection of the frame. During the last 60 decades, a large number of experimental studies have been carried out on frame assemblies, where various parameters and their compatibility under cyclic activities have been investigated. What remains misunderstood is the magnitude and distribution of the forces passing through the joint and their involvement in the magnitude of the shear force. Here, the creation of a new mathematical model for the beam and column contributes significantly to our understanding of the flow of forces in the frame connection. For this purpose, the full dimensions of the beam and its material properties are taken into account. All investigations were carried out before crack initiation and after crack propagation along the face of the column, where it separates from the beam. In the present work, the beam is subjected to two symmetrical, transverse, uniformly distributed loads. Expressions are derived to determine the magnitudes of the support reactions from the beam, as a function of the height of its lateral edge. The load positions corresponding to the extreme values of the support reactions are determined. Numerical results are presented for the effect over the magnitudes of the support reactions from different strengths of concrete and steel on the beam. The results are compared with those given in the Eurocode for shear force calculation. It is found that the shear force determined by the proposed new model exceeds the force calculated by Eurocode by 4-62.5%, depending on the crack development stage and the beam materials.
Results of an experimental investigation on the behavior and ultimate shear capacity of 27 reinforced concrete Transfer (deep) beams are summarized. The main variables were percent longitudinal (tension) steel (0.28 to 0.60%), percent horizontal web steel (0.60 to 2.40%), percent vertical steel (0.50 to 2.25%), percent orthogonal web steel, shear span-to-depth ratio (1.10 to 3.20) and cube concrete compressive strength (32 MPa to 48 MPa).The span of the beam has been kept constant at 1000 mm with 100 mm overhang on either side of the supports. The result of this study shows that the load transfer capacity of transfer (deep) beam with distributed longitudinal reinforcement is increased significantly. Also, the vertical shear reinforcement is more effective than the horizontal reinforcement in increasing the shear capacity as well as to transform the brittle mode of failure in to the ductile mode of failure. It has been observed that the orthogonal web reinforcement is highly influencing parameter to generate the shear capacity of transfer beams as well as its failure modes. Moreover, the results from the experiments have been processed suitably and presented an analytical model for design of transfer beams in high-rise buildings for estimating the shear capacity of beams.
European Journal of Wood and Wood Products, 2011
The elastic -full plastic loading curve is for all materials sufficient to explain the strength of beams and beam columns loaded by bending and compression. This theory is extended for the influence of shear stress, and it is shown to be the only way to explain the combined bending-shear strength from test results. Also, the in the past derived bearing strength theory is extended here for bracing action. It will be shown for continuous beams as example, that besides moment redistribution by plastic flow in bending, a plastic shear flow mechanism exists that is also able to cause full moment redistribution. The derivations lead to requirements for the design rules and show how the shear stress may reduce the ultimate bending capacity.
Shear Strengthening of T-beam with GFRP, 2018
Finite element method (FEM) is used to study the behaviour of RC T-beams strengthened in shear with GFRP sheet under two-point loading condition. The finite element analysis is carried out in this study using ANSYS finite element software. Specimens without GFRP as control beams, designated as S0-0L, S300-0L and S200-0L and beams strengthened with GFRP sheets in U-jacket for specimens S0-1L-CT-U-90, S300-1L-CT-U-90 and S200-1L-CT-U-90 (Panda et al. 2012) are analysed. The main focus of the chapter is on the development of the model for full-size beams, elements used for the development of the model, geometry of the models, loading and boundary conditions and comparison of results with experiment. The formulation of the FEM models is discussed in the following sections. 6.2 Element Formulation Commercially available ANSYS software has been used for the numerical study. The elements selected for the study are described below. 6.2.1 Reinforced Concrete Solid65 is an eight-noded solid element with three degrees of freedom at each node and translations in the x, y and z directions. This element is used to model the concrete beams with or without steel reinforcement bars. The solid element is capable of representing plastic deformation, cracking in three orthogonal directions and also crushing of concrete. Isotropic material properties are considered for the elements (Kachlakev et al. 2001). The geometry of Solid65 element is shown in Fig. 6.1.
Advances in Computer Science and IT, 2009
The organization of this chapter mimics that of the last chapter on torsion of circular shafts but the story about stresses in beams is longer, covers more territory, and is a bit more complex. In torsion of a circular shaft, the action was all shear; contiguous cross sections sheared over one another in their rotation about the axis of the shaft. Here, the major stresses induced due to bending are normal stresses of tension and compression. But the state of stress within the beam includes shear stresses due to the shear force in addition to the major normal stresses due to bending although the former are generally of smaller order when compared to the latter. Still, in some contexts shear components of stress must be considered if failure is to be avoided. Our study of the deflections of a shaft in torsion produced a relationship between the applied torque and the angular rotation of one end of the shaft about its longitudinal axis relative to the other end of the shaft. This had the form of a stiffness equation for a linear spring, or truss member loaded in tension, i.e., M T = (GJ ⁄ L) φ ⋅ is like F = (AE ⁄ L) δ ⋅ Similarly, the rate of rotation of circular cross sections was a constant along the shaft just as the rate of displacement if you like, ∂ u , the extensional strain ∂ x was constant along the truss member loaded solely at its ends. We will construct a similar relationship between the moment and the radius of curvature of the beam in bending as a step along the path to fixing the normal stress distribution. We must go further if we wish to determine the transverse displacement and slope of the beam's longitudinal axis. The deflected shape will generally vary as we move along the axis of the beam, and how it varies will depend upon how the loading is distributed over the span Note that we could have considered a torque per unit length distributed over the shaft in torsion and made our life more complex – the rate of rotation, the dφ /dz would then not be constant along the shaft. In subsequent chapters, we derive and solve a differential equation for the transverse displacement as a function of position along the beam. Our exploration of the behavior of beams will include a look at how they might buckle. Buckling is a mode of failure that can occur when member loads are well below the yield or fracture strength. Our prediction of critical buckling loads will again come from a study of the deflections of the beam, but now we must consider the possibility of relatively large deflections.
