After the progressive collapse of Ronan Point apartment in UK in 1968, intensive research effort had been spent on developing guidelines for design of new or strengthening the existing structures to prevent progressiv...After the progressive collapse of Ronan Point apartment in UK in 1968, intensive research effort had been spent on developing guidelines for design of new or strengthening the existing structures to prevent progressive collapse. However, only very few building design codes provide some rather general guidance, no detailed design requirement is given. Progressive collapse of the Alfred P. Murrah Federal building in Oklahoma City and the World Trade Centre (WTC) sparked again tremendous research interest on progressive collapse of structures. Recently, US Department of Defence (DoD) and US General Service Administration (GSA) issued guidelines for structure progressive collapse analysis. These two guidelines are most commonly used, but their accuracy is not known. This paper presents numerical analysis of progressive collapse of an example frame structure to blast loads. The DoD and GSA procedures are also used to analyse the same example structure. Numerical results are compared and discussed. The accuracy and the applicability of the two design guidelines are evaluated.展开更多
Let ,4 = {1 ≤ a1 〈 a2 〈 ...} be a sequence of integers. ,4 is called a sum-free sequence if no ai is the sum of two or more distinct earlier terms. Let A be the supremum of reciprocal sums of sum-free sequences. In...Let ,4 = {1 ≤ a1 〈 a2 〈 ...} be a sequence of integers. ,4 is called a sum-free sequence if no ai is the sum of two or more distinct earlier terms. Let A be the supremum of reciprocal sums of sum-free sequences. In 1962, ErdSs proved that A 〈 103. A sum-free sequence must satisfy an ≥ （k ~ 1）（n - ak） for all k, n ≥ 1. A sequence satisfying this inequality is called a x-sequence. In 1977, Levine and O＇Sullivan proved that a x-sequence A with a large reciprocal sum must have al = 1, a2 = 2, and a3 = 4. This can be used to prove that λ 〈 4. In this paper, it is proved that a x-sequence A with a large reciprocal sum must have its initial 16 terms： 1, 2, 4, 6, 9, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, and 50. This together with some new techniques can be used to prove that λ 〈 3.0752. Three conjectures are posed.展开更多
An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of element...An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of elements is∑1/ai〉 2.065436491, which improves slightly the related upper bounds for the reciprocal sums of sum-free sequences.展开更多
基金Supported by National Natural Science Foundation of China(No.50528808)Australian Research Council(No. DP0451966)
文摘After the progressive collapse of Ronan Point apartment in UK in 1968, intensive research effort had been spent on developing guidelines for design of new or strengthening the existing structures to prevent progressive collapse. However, only very few building design codes provide some rather general guidance, no detailed design requirement is given. Progressive collapse of the Alfred P. Murrah Federal building in Oklahoma City and the World Trade Centre (WTC) sparked again tremendous research interest on progressive collapse of structures. Recently, US Department of Defence (DoD) and US General Service Administration (GSA) issued guidelines for structure progressive collapse analysis. These two guidelines are most commonly used, but their accuracy is not known. This paper presents numerical analysis of progressive collapse of an example frame structure to blast loads. The DoD and GSA procedures are also used to analyse the same example structure. Numerical results are compared and discussed. The accuracy and the applicability of the two design guidelines are evaluated.
基金supported by National Natural Science Foundation of China(Grant No.11071121)
文摘Let ,4 = {1 ≤ a1 〈 a2 〈 ...} be a sequence of integers. ,4 is called a sum-free sequence if no ai is the sum of two or more distinct earlier terms. Let A be the supremum of reciprocal sums of sum-free sequences. In 1962, ErdSs proved that A 〈 103. A sum-free sequence must satisfy an ≥ （k ~ 1）（n - ak） for all k, n ≥ 1. A sequence satisfying this inequality is called a x-sequence. In 1977, Levine and O＇Sullivan proved that a x-sequence A with a large reciprocal sum must have al = 1, a2 = 2, and a3 = 4. This can be used to prove that λ 〈 4. In this paper, it is proved that a x-sequence A with a large reciprocal sum must have its initial 16 terms： 1, 2, 4, 6, 9, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, and 50. This together with some new techniques can be used to prove that λ 〈 3.0752. Three conjectures are posed.
基金the Natural Science Foundation of the Education Department of Sichuan Province (No.2006C057)
文摘An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of elements is∑1/ai〉 2.065436491, which improves slightly the related upper bounds for the reciprocal sums of sum-free sequences.
