Chapter 4
Bending
Bending: Bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
Bending stress: Bending stresses are those that bend the beam because of beam self-load and external load acting on it.
Beam is a structural member which is subjected to transverse load only.
Support and its types
Support is important aspect of structure while solving any any problem , support specify that how the forces within structure is transffered to the ground. It ultimetly tells us the boundary conditions while solving any finite element model.various supports are Fixed support-A fixed support is the most rigid support. It constrains
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This loading causes the member to bend and deflect from the original position with internal tensile and compressive strain.
Degree of freedom- Degree of freedom of a point is possible moment of that point due to loading in structure. Six possible degree of freedom for the element which are -
Translation in X, Y and Z direction. Rotation in X, Y and Z direction.
Types of loads- two types of loads are given below
Point load-load which is act on a point or location of body is point load
Uniformly distributed load- UDL is a kind of load which is spread over entire span of body or over a particular portion of the beam in some specific manner.
Uniformly varying load-UVL is load which spread over the length of body in such manner that load intensity varies at point to point along the length of body.
Simply supported beam is a beam supported on the both ends which are free to rotate. Bikes and bicycles are the daily life examples of this kind of beam
Cantilever beam is a beam which is fixing at one end and free at other end. Motorcycle kick is also example of cantilever
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Beam and max deflection of beams:
Beam type Loading on beam Maximum deflection on beam
Cantilever Beam with load P at the free end _max= (P l^3)/3EI
Cantilever Beam with UDL _max= (w l^4)/(8 EI)
Simply Supported beam with load P at the centre _max= (P l^3)/(48 EI)
Simply Supported beam with UDL _max= (5w l^4)/(384 EI)
Types of load- two types of loads are given below Workshop 6 beam with all cases
Pure bending is a condition of stress where a bending moment is applied to a beam without the presence of axial, shear or torsional forces.
Theory of simple bending(Assumptions) Material of beam is homogenous and Isotropic, Constant E in all direction Youngs Modulus will be constant in compression and tension. Transverse sections which are plain before bending remains plain after bending i.e eliminate strains in other directions. Initially beam is straight and all longitudinal filaments bend in circular arcs. Radius of curvature is larger compared with the Dimension of the cross section. Each layer of the beam is free to expand or contract otherwise they will generate internal
A simple beam bridge that is flat across and supported at the two ends. A longer beam bridge can be held up along the middle by piers standing in the river. The weight of the bridge itself, plus the load that it carries, plus gravity are the downward forces are spread evenly across the length of the bridge. The upwards forces that hold the bridge up come from the piers. The Confederation Bridge in Canada is a famous beam bridge.
A load path is the transfer of loads and forces from the through the building to the bottom of the building, following the most direct structural path.
{N} and {M} are the generalised stresses can can be expressed as membrane strains and curvatures by using the laminar stress-strain relationship and Love Kirchhoff hypothesis.
Arielle: (show drawing) In the end we had made a beam bridge out of hot glue, cardboard and popsicle sticks. We used the cardboard because it is a flat surface and is very light. However, cardboard is not strong enough on it’s own. We then decided to use hot glue to attach the popsicle sticks to the
Adduction is the movement of a body segment towards the midline of the body. The example of this would be the return of the cable lateral raise back towards the center of the body.
This report has been written to describe an experiment performed on a channel section examining the stiffness of the beam through two differing types of deformation – curvature and deflection. The aim of the experiment was to determine the value of the flexural rigidity (EI) in two different ways; using the curvature, k, and the mid-span deflection. The testing method used for the experiment is described. The experiment found that the EI values calculated were as follows: - EIcurv = 1.76E+10 Mpa.mm4 when calculated using the curvature, k. - EIdefl
In this lab, deflection and strain are measured in an attempt to confirm Hooke’s law and the Euler-Bernoulli bending beam theory. In addition, the measured data allows us to calculate the modulus of elasticity (Young’s Modulus) or E of the cantilever beam. Through the course of the experiment our observations revealed that the addition of weights deformed the beam in response to the applied stress. This deformation can be modeled using the Euler-Bernoulli beam bending theory. Our experimentation and calculations revealed that our data did indeed prove the theories mentioned in this lab. Furthermore, our values for the modulus of elasticity or E came within the range of established values found online.
The web of the prefabricated truss can be analyzed as a column. Burdzik analyzed the web of a truss as a non-continuous compression member. Columns must take the effective length into account for both the in plane and out of plane bending. The connection type, continuity, and capacity of adjacent members affect the degree of restraint for the web member (Burdzik,
There are three sorts of statically determinate trusses, which are immediate, compound, and complex. (Stray pieces, n.d.)
The experiment we chose to accomplish was to test trusses and observe which upheld the most weight. Obvious constraints were placed on this, as it was not just open-ended. All trusses were to be based off the same design, with just the addition of more vertical beams on various trusses, the number of beams incrementing steadily.
where K is the stiffness matrix, ∆d is the vector of displacements, and ∆P is a load vector resulting from the imposed boundary conditions, induced pressure and temperature changes.
These bridges are made of trusses, which are patterns of triangles. The truss was developed during the Industrial Revolution when people were finding ways to develop better girder bridges. These trusses are now used to stabilize and support other bridges, such as suspension bridges. Trusses are used widely because the truss pattern is rigid and can dissipate weight throughout the truss. They can be commonly found on girder bridges, because the truss pattern evens out the forces of tension and compression. A deck truss, a type of truss bridge, is classified by having its roadway above the truss. A through truss is another type of truss bridge that has the truss above the roadway. There are various types of truss patterns, which include the K truss, the Pratt truss, the Warren truss, and the Howe
Superstructure bears the load that is being passed over the bridge and it transmits the forces caused by the same to substructure. Load received from the decking is transferred on to the substructure by Bearings. They also distribute the load evenly over the substructure material as it may not have sufficient strength to bear the superstructure load directly. Piers and Abutments are the vertical substructures which transfer the load to the earth in the foundation. Wing walls and returns are constructed as the extension of
Purpose: The purpose of this Physics Lab is to investigate what factors determine the amount of flexion of the cantilever. Hence, the objective is to establish a relationship between the length of a cantilever, which may give some insight into the physics of cantilevers.
The objective of this experiment is to demonstrate the bending of a bean when loaded at the center of its length and examine its deflection when positioned in two different ways, when the flat side of the beam is support and when the thin side is supported. In addition, try to find linear relationship between the load applied and the deflection of the beam and comparing the experimental deflection with the theoretical deflection.