China
Africa
Explore chapters and articles related to this topic
Mechanics of Structures and Their Analysis
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
The rotation, inclination, and deflection of beams and frames are derived from the moment area theorem. The theorem was formulated by Otto Mohr and disclosed later in 1873 by Charles Greene. In this technique, area of the BMD is considered for the measurement of the slope and/or the deflections along the axis of the beam or frame at any point. For the computation of the deflection, two theorems known as the moment area theorems are used. One theorem is used to compute the change of slope in the elastic curve between two points. While the other theorem is used to compute the vertical distance between a point on the elastic curve and a line tangent to the elastic curve at a second point (called tangential deviation). For this purpose, the bending moment chart for the beam is first drawn and then divided by the flexural rigidity (EI) to obtain the “M/EI” chart.
Deflection and Impact
Published in Ansel C. Ugural, Youngjin Chung, Errol A. Ugural, Mechanical Engineering Design, 2020
Ansel C. Ugural, Youngjin Chung, Errol A. Ugural
Two theorems form the basis of the moment-area approach. These principles are developed by considering a segment AB of the deflection curve of a beam under an arbitrary loading. The sketches of the M/EI diagram and the greatly exaggerated deflection curve are shown in Figure 4.10a. Here, M is the bending moment in the beam and EI represents the flexural rigidity. The changes in the angle dθ of the tangents at the ends of an element of length dx and the bending moment are connected through Equations (4.14) and (4.15): dθ=MEIdx
Deflection and Impact
Published in Ansel C. Ugural, Youngjin Chung, Errol A. Ugural, MECHANICAL DESIGN of Machine Components, 2018
Ansel C. Ugural, Youngjin Chung, Errol A. Ugural
Two theorems form the basis of the moment-area approach. These principles are developed by considering a segment AB of the deflection curve of a beam under an arbitrary loading. The sketches of the M/EI diagram and greatly exaggerated deflection curve are shown in Figure 4.12a. Here, M is the bending moment in the beam and EI represents the flexural rigidity. The changes in the angle dθ of the tangents at the ends of an element of length dx and the bending moment are connected through Equations 4.14 and 4.15: () dθ=MEIdx
Time-dependent reliability analysis for a set of RC T-beam bridges under realistic traffic considering creep and shrinkage
Published in European Journal of Environmental and Civil Engineering, 2022
Fatima El Hajj Chehade, Rafic Younes, Hussein Mroueh, Fadi Hage Chehade
The in-service deflection ycalc can be deduced by double integration from the time-dependent load induced and shrinkage induced curvature. It is related to the applied load by the effective flexural rigidity or flexural stiffness EcIef whose degradation affects the reliability of the structure. where δz is the deflection at location z and κ(x) is the curvature at any location x along the member. However, analytical computation of this double integration is very complicated since curvature depends on time and location. This operation is simplified by assuming parabolic variation between adjacent points. Midspan deflection can then be expressed in terms of curvatures at three critical positions: left and right supports and midspan in case of simply supported beam (Khor et al., 2001) where δmidspan is the midspan deflection, L is the span length, κL, κM and κR are the curvatures at left support, midspan and right support respectively.
Silica nanocomposite based hydrophobic functionality on jute textiles
Published in The Journal of The Textile Institute, 2021
Lakshmanan Ammayappan, Sujay Chakraborty, Nimai Chandra Pan
Flexural rigidity is a resistance of fabric against bending by external forces and it correlates with bending length and weight per unit area. Jute fibre has an inherent stiffness so that the bleached jute fabric has shown a high flexural rigidity (35μN.m). After each finishing process, the flexural rigidity of the jute fabric is reduced @ ≥50% and the percentage reduction is higher (57%) in 0.25% silica nano sol + 20gpL NUVA finishing and lesser (47%) in 2.0% silica nano sol finishing than the bleached jute fabric. During padding, the jute fabric was subjected to flattening; during curing, the crystalline portion of the fibre may be weakened slightly; and during NUVA finishing, the coated polymer may further reduce the stiffness of the fibrils. These factors are responsible for the reduction in the flexural rigidity of silica nano sol finished jute fabrics.
Implications of environmental conditions for health status and biomechanics of freshwater macrophytes in hydraulic laboratories
Published in Journal of Ecohydraulics, 2020
Davide Vettori, Stephen P. Rice
Mechanical tests were conducted using a benchtop testing machine (Instron Single Column 3343, Instron, High Wycombe, UK) equipped with a 50 N load cell. Tests were conducted with a displacement rate equal to 10 mm min–1 and lasted <1 min. The manufacturer reports an accuracy of the force readings of 0.5% and that of displacement readings of 1%. To minimize end-wall effects, samples for uniaxial tensile tests were prepared with a diameter to length ratio lower than 1:10 (Niklas 1992; Niklas and Spatz 2012). Sample ends were positioned within screw side-action grips and were protected using small metal pipes to preserve sample integrity during the tests (Miler et al. 2012). Samples for flexural tests were prepared with a diameter-to-span ratio as low as possible to minimize shear effects, bearing in mind that this ratio is recommended to be lower than 1:15 (Usherwood et al. 1997; Miler et al. 2012). To perform 3-point flexural tests, sample ends were supported at each end by two lower anvils, while an upper anvil applied a load at the center. For tensile tests, data of force and displacement were converted into nominal stress and strain from which the tensile Young’s modulus was calculated as the slope of the linear (elastic) part of the stress–strain curve (Figure 3(a)). From 3-point flexural tests, data of force and displacement were used to calculate the flexural rigidity using the formula where is the flexural Young’s modulus, is the moment of inertia, is the sample span, and is the slope of the initial part of the force–displacement curve (Figure 3(b)).