A Note on the Bending Moment Induced in the Booms of a Spar at the Point of Application of a Concentrated Load

1950 ◽  
Vol 1 (4) ◽  
pp. 281-290
Author(s):  
H. F. Winny
Keyword(s):  
Shear Strain ◽  
Experimental Verification ◽  
Mathematical Theory ◽  
Bending Moment ◽  
Wave Form ◽  
Concentrated Load ◽  
Original Investigation ◽  
Wing Spar ◽  
The Web

SummaryThe effect of a concentrated load, such as occurs in a wing spar at the fuselage, is to cause a discontinuity in shear strain of the spar web, which induces a bending moment in the booms through the medium of the rivets (or bolts) which attach the booms to the web. A mathematical theory is developed which shows that this bending induced in the boom is of a damped wave form starting at the point of application of the shear, and in practice the magnitude of the stresses produced by the bending moment may be appreciable at the wing root when the boom is deep compared with the spar depth (say 20 per cent.).Further experimental verification is desirable, but a single wing test suggested the original investigation, and showed a measure of agreement with the theory.

The Twist Due To Bending Moment in Cantilevers Curved in flan

1956 ◽  
Vol 60 (544) ◽  
pp. 277-281
Author(s):  
W. Johnson
Keyword(s):  
Constant Curvature ◽  
Vertical Plane ◽  
Bending Moment ◽  
Shear Stresses ◽  
Bending Moments ◽  
Concentrated Load ◽  
Bending Stresses ◽  
Thin Walled ◽  
Shear Centre ◽  
The Web

The twist that arises from bending stresses in straight cantilevers of thin-walled section asymmetrical about any vertical plane, is well known and eventually leads to the concept of a shear centre. If an analysis is made along the same lines as that used for investigating straight beams, of cantilevers curved in plan, it is found that the bending moments transmitted are again responsible for shear stresses in the flanges of the beam and cause twisting.The following analyses refer, principally, to cases in which the cantilever carries a concentrated load at its end and are confined to the relatively simple forms of the channel and I-section. Each cantilever is perfectly built-in at one end and, for simplicity, it is considered that the web of a section offers no resistance to bending and that the beams are of constant curvature in plan.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

The Signal Generated by an Insect in a Spider's Web

1965 ◽  
Vol 43 (1) ◽  
pp. 185-192
Author(s):  
D. A. PARRY
Keyword(s):  
Linear Response ◽  
Wave Form ◽  
Irregular Wave ◽  
Prey Recognition ◽  
Upper Limit ◽  
Fast Transients ◽  
Sudden Release ◽  
House Spider ◽  
Rotational Oscillations ◽  
The Web

1. There is evidence that web-spinning spiders discriminate between prey and artifacts in their webs, and that the signal involved is a mechanical one. As a contribution to our understanding of the basis of this discrimination, an analysis has been made of the natural signal generated by an insect in the web of the British house spider Tegenaria atrica. 2. The signal investigated was frequency-limited to 1 kc./sec, this being the upper limit of the linear response of the specially designed transducer. 3. The signal has an irregular wave-form with most of the energy lying below 50 cyc./sec. Damped transverse and rotational oscillations of the mass of the spider in the compliance of the web have been recognized. In addition there are ‘fast transients’, most likely due to the sudden release of tension in the web by slight movements of the insect. 4. The possibility that the fast transients form the basis of prey-recognition is being investigated.

Study on Prediction Deflection of at the Girder Midspan of Large Tonnage Gantry Crane Rigid Legs

2014 ◽  
Vol 628 ◽  
pp. 214-218
Author(s):  
Da Peng Zhang ◽  
Wen Ming Cheng ◽  
Kun Cai
Keyword(s):  
Bending Moment ◽  
Moment Of Inertia ◽  
Load Test ◽  
Test Method ◽  
Gantry Crane ◽  
Deflection Curve ◽  
Concentrated Load ◽  
Small Load ◽  
Curve Equation

It is the most important inspection index of the deflection value for the girder of gantry crane under rated load in the overall test. In the overall test for large tonnage gantry crane which prepared for experimental weight is very difficult at the site, or even impossible perform test. In the text, it is deduced the girder deflection curve equation where considering the effects of the leg bending moment to the girder deflection When the concentrated load is applied to the position of L/2,L/3 and 2L/3 of the girder. The girder deflection value can be obtained under small load at the position of L/2,L/3 and 2L/3 of the girder and the actual moment of inertia of the girder and two side leg can be obtained. In this way, the deflection of the large tonnage gantry crane are predicted through the data of the three-position method in the small load test. Three-position small load test method provides a practical and effective method for the prediction of the girder deflection of large tonnage gantry structure.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

Why Shear Webs?

1948 ◽  
Vol 52 (455) ◽  
pp. 759-761
Author(s):  
H. L. Cox
Keyword(s):  
Small Angle ◽  
Bending Moment ◽  
Shear Load ◽  
The Web

At a section of a cantilever distant x from its tip, let the depth of section be h and the bending moment M. Then if all the resistance to bending is concentrated in the flanges the loads in the flanges are ±M/h. If the flanges are inclined at a small angle α these flange loads have a component transverse to the cantilever axis of magnitude Mα/h. Now α=dh/dx and the shear load at section x is dM/dx. Therefore the shear load on the web of the cantilever is dM/dx-(M/h)dh/dx, and, if h/M is constant, the web is not sheared at all.

Performance of micropiled raft in sand subjected to vertical concentrated load: centrifuge modeling

2015 ◽  
Vol 52 (1) ◽  
pp. 33-45 ◽  
Author(s):  
A.M. Alnuaim ◽  
H. El Naggar ◽  
M.H. El Naggar
Keyword(s):  
Contact Pressure ◽  
Bending Moment ◽  
Centrifuge Modeling ◽  
Design Parameters ◽  
Concentrated Load ◽  
Centrifuge Testing ◽  
Geotechnical Centrifuge ◽  
Piled Raft Foundation ◽  
Overall Performance ◽  
Important Design

Initial applications of micropiles have involved retrofitting foundations of existing buildings. In these applications, the overall performance of the micropiles–raft (MPR) foundation system is similar to a piled raft foundation where the load is transmitted through both the raft and micropiles. However, there is no guidance available regarding the performance of MPR foundations. In this study, geotechnical centrifuge testing was conducted to investigate the behavior of MPR foundations in sand and evaluate their performance characteristics. The study investigated the effect of raft flexibility on a number of important design parameters, including raft total and differential settlements, raft contact pressure, raft bending moment, and load sharing between the raft and micropiles. In addition, the use of micropiles as settlement reducers was investigated. The results showed that the micropiles carried 42%–59% of the applied load for the MPR configuration considered, which resulted in redistribution of the raft contact pressure. It was found that the Poulos–Davis–Randolph (PDR) method can be used to evaluate the performance of MPR systems with relatively stiff rafts; however, it is not applicable for MPR with flexible raft. A correction factor was proposed to account for the raft flexibility in the PDR method.

The stresses in a built-up girder subjected to a concentrated load

1955 ◽  
Vol 231 (1186) ◽  
pp. 379-387
Keyword(s):  
Plane Stress ◽  
Constant Thickness ◽  
Concentrated Load ◽  
The Web

An analysis is given for the stresses in a uniform built-up girder consisting of a web of constant thickness elastically connected to two similar flanges. The flanges are assumed to obey the Bemoulli-Euler theory of bending; the web is treated as a problem in plane stress. The method can be used for any type of flange loading, but particular application is limited to a single concentrated load applied to one flange. A cantilever built-up girder subjected to this type of load has been investigated experimentally at the College of Aeronautics, Cranfield, and comparison is made between the theoretical and experimental stresses.

Performance of micropiled raft in clay subjected to vertical concentrated load: centrifuge modeling

2015 ◽  
Vol 52 (12) ◽  
pp. 2017-2029 ◽  
Author(s):  
A.M. Alnuaim ◽  
M.H. El Naggar ◽  
H. El Naggar
Keyword(s):  
Contact Pressure ◽  
Applied Load ◽  
Bending Moment ◽  
Centrifuge Modeling ◽  
Performance Characteristics ◽  
Concentrated Load ◽  
Centrifuge Testing ◽  
Geotechnical Centrifuge ◽  
Piled Raft Foundation ◽  
Raft Foundation

The overall behavior of a micropiled raft foundation (MPR) system is similar to a piled raft foundation where the load is transferred by both the raft and micropiles. However, there is no guidance available regarding the design of MPRs or indication of their performance. In this study, geotechnical centrifuge testing was conducted to investigate the behavior of MPR foundations in clay and evaluate their performance characteristics. The study evaluated the performance of MPRs compared to the isolated raft in terms of raft total and differential settlements; raft contact pressure; raft bending moment; and load sharing between the raft and the micropiles. The results showed that for the MPR configuration considered in the study, the raft carried 48% of the applied load. It was found that the Poulos–Davis–Randolph (PDR) method can be used to evaluate the performance of MPR for preliminarily design purposes with approximately 17% error.

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