On the diophantine equation $(x+1)^2+(x+2)^2+...+(x+d)^2=y^n$

Zhang, Zhongfeng; Meng, Bo

doi:10.7169/facm/2013.49.1.4

Cited by 16 publications

(19 citation statements)

References 5 publications

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“…The longitudinal displacement caused by the axial force only happens in I-shaped shear walls, and it is zero for I-shaped beams. The shear lag warping displacement is assumed to be a quadratic parabola, and the additional deflection caused by shear lag effect is chosen as the generalized displacement, [16] thus the longitudinal displacement u(x,y,z) of the cross section can be expressed as follows:…”

Section: Basic Assumptionsmentioning

confidence: 99%

“…w ξ (x, y) is assumed as a quadratic parabola. [16,17] The shear lag effect of the web can be ignored because of its small thickness. The shear lag warping displacement w ξ (x, y) of the cross section can be expressed as Equation 3:…”

Section: Basic Assumptionsmentioning

confidence: 99%

“…The bending moment acting on the cross sections of I-shaped structural members is only dependent on the normal stress of elementary beam theory, which means that shear lag warping stress σ w needs to meet the two self-balancing conditions [16] :…”

Section: Total Potential Energy Functionsmentioning

confidence: 99%

“…When F > 0, the top flange is in tension, and the bottom flange is in compression; when F < 0, the top flange is in compression, and the bottom flange is in tension. The external potential energy V p of I-shaped shear walls can be expressed as Equation 16:…”

Section: Analytical Solutions Of I-shaped Shear Wallsmentioning

confidence: 99%

“…By substituting Equation 16 into Equation 13, the total potential energy of I-shaped shear walls can be obtained and expressed as Equation 17:…”

Section: Analytical Solutions Of I-shaped Shear Wallsmentioning

confidence: 99%

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Shear lag analysis of I‐shaped structural members

Cao

2018

Structural Design Tall Build

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Summary I‐shaped structural members are widely used in civil engineering, mainly including I‐shaped shear walls and beams. In order to establish a unified method for analyzing the shear lag effect of I‐shaped structural members, first, the shear lag warping displacement is assumed as a quadratic parabola, and the additional deflection caused by shear lag effect is taken as the generalized displacement. The principle of minimum potential energy is used to establish the calculation method of the normal stress and deflection of I‐shaped shear walls and beams with 3 boundaries, which consider the self‐balancing conditions of shear lag warping stress. Then numerical examples are used to verify the accuracy of the calculation method; meanwhile, the shear lag characteristics of I‐shaped structural members are investigated. At last, the calculation method is used to study the shear lag effect of T‐shaped structural members. Studies show that the analytical results obtained by the calculation method are close to the finite element method results, and the calculation method can predict the flange normal stresses and negative shear lag phenomenon well. Moreover, the calculation method in this paper can be used to analyze the shear lag of T‐shaped structural members.

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Section: Basic Assumptionsmentioning

confidence: 99%

Section: Basic Assumptionsmentioning

confidence: 99%

Section: Total Potential Energy Functionsmentioning

confidence: 99%

Section: Analytical Solutions Of I-shaped Shear Wallsmentioning

confidence: 99%

“…By substituting Equation 16 into Equation 13, the total potential energy of I-shaped shear walls can be obtained and expressed as Equation 17:…”

Section: Analytical Solutions Of I-shaped Shear Wallsmentioning

confidence: 99%