Internal Force System and Current Secondary Moment Concept in Prestressed Structures

For plane truss structure, starting from the analysis of ideal truss model, the influence of tangential deformation and angular deformation on the secondary internal force of the truss is fully considered through Python program. It is obtained through analysis that: in the ideal truss model, the Pδ second-order effect causes the member to produce tangential deformation and angular deformation, resulting in secondary internal forces. Numerical analysis shows that due to the influence of secondary internal force, the axial force error of ideal truss model can reach 19.731% and the secondary shear force is almost all the members of the truss, and the secondary moment only appears at the support. The research results have important reference value for the engineering design and high-precision internal force analysis of truss structures.

The work addresses studying the possibilities of a numerical-analytical variant of the boundary elements method (BEM) in determining the internal force factors and stresses at singular points when bending thin isotropic plates. The simplest type of singularity has been investigated, a point of application of external concentrated forces and moments. The importance of a given problem is due to the fact that at these points the internal force factors tend towards infinity and it is not possible to determine the size using elementary methods. At the same time, these singular points are the significant stress concentrators (both tangential and normal), which is why calculating the limits to which the internal forces and moments tend is essential to analyze the strength of plate structures. In order to describe an external load, it is proposed to apply the Dirac delta function of two variables. The models of external loads are presented. A given proposal makes it possible to accurately calculate the limits to which the transverse forces, as well as bending and torsional moments, tend at singular points of thin plates. We simulated plate bending using the variational Kantorovich-Vlasov method, which is fully compatible with the models of external load. The internal force factors at the singular points of plates were determined while solving the boundary value problems, formed based on the algorithm of BEM. The MATLAB environment was used for programming and computation. Results of the calculations are characterized by high accuracy and reliability, in particular the errors in determining the deflections of plates at singular points do not exceed 2.0 % and the errors for bending moments are not above 3.0 %. Recommendations have been given to solving different types of boundary problems on bending the plates with singular points based on the proposed approach. It has been established that an accurate model of the external load in the form of concentrated forces and moments fundamentally enables determining the internal forces and moments at the singular points of thin plates applying an algorithm of the variational Kantorovich-Vlasov method. Up to now, there are no data on the importance of internal forces and moments at the singular points of plates. It is also shown that when calculating the internal forces and moments of plates, it is inappropriate to apply a single term from a series of the Kantorovich-Vlasov method; the errors amount to significant magnitudes of the order of 43‒44 %

We demonstrate that the internal forces and moments in a shell structure can be described by 4 vectors in 3 dimensional space which could be used to express the equilibrium of a shell graphically. The internal forces and moments described by 2 of the 4 vectors actively carry imposed loads and imposed couples, while the other 2 describe ‘redundant’ internal forces and moments that are purely in equilibrium with themselves. Nevertheless redundant stresses and moments are important in controlling internal stresses and satisfying boundary conditions. We show that forces and moments ‘flow’ across a shell in exactly the same way that fluid flows, with a combination of irrotational flow and incompressible flow. The aim is that these ideas can help in the initial design of those shell structures which have to rely on bending moments in addition to membrane action in supporting loads, and also in the interpretation of results from an analysis using the finite element method. We demonstrate the use of the technique for the design of an umbrella structure like those built by Amancio Williams.

Analysis on the stiffness iteration of segmental joints in segmental linings: Method and sensitivity analysis

To explore the impact of ground load on existing shield tunnels and connected shaft structures, this study designed a testing device to identify the stress of shield tunnels and connected shaft structures under ground load. By controlling the location and magnitude of the load, we investigated the internal forces and deformations of the tunnels and shafts, as well as the displacement of the soil. Additionally, a three‐dimensional finite element model was established to reveal the internal forces and deformations of shield tunnels and connected shaft structures under uniform ground load, as well as the settlement of the soil. The finite element simulation results were highly consistent with the results of indoor model tests, demonstrating the consistency between these two methods. The results indicated that the internal forces and deformations of the shafts vary significantly with the magnitude of the surcharge load. When the surcharge is directly above the tunnel axis, the internal forces of the shafts decrease as the distance between the load and the shaft increases. Within the 2D eccentric range, the internal force changes caused by the load effect are significant, but outside the 3D eccentric range, the internal forces and bending moments of the shafts decrease significantly, and the magnitude of the changes is not obvious. Beyond the 2D range of the load area, the displacement of the soil decreases significantly, and the magnitude of the changes is not obvious. This reflects the significant impact of ground load on the shaft structure and highlights the tolerance of remote soil measurement points to load fluctuations. This study has strong reference significance for the excavation of vertical pipelines under shield tunnels.

Manufacturing errors in the length of members or joint diameters of large truss reflector backup structures may result in unacceptable large distortion errors or member forces. However, it may be possible to accurately measure these length or diameter errors. The present work suggests that a member and joint placement strategy may be used to reduce distortion errors and internal member forces. A member and joint exchange algorithm is used to demonstrate the potential of this approach on several 102-member and 660-member truss reflector structures. It is shown that it is possible to simultaneously reduce the rms of the surface error and the rms of member forces by two orders of magnitude by member and joint exchanges.

The secondary internal force caused by temperature in statically indeterminate bridges are usually huge, sometime is the control factor in bridge design. Since the temperature investigation of bridge construction site is difficult to predict, there deviation between design joining temperature and actual temperature and the leaded secondary internal force is inevitable. Based on this, an adaptive temperature internal force control method is proposed. This method utilizes a pre-set steel cable. When the environmental temperature changes produce negative effects to the structure, the additional force and moment of cable with the change of environment temperature will offset the effect. This method can be widely used in the temperature internal force control of statically indeterminate bridge structures, and can effectively reduce the additional internal force of undetermined bridge structures caused by temperature differences.

Through predict activities trend of ground fissures, given to the ground surface subsidence curve on the topper side in the next 50 years. Established a tall concrete frame construction model, using SAP2000 finite element programs, take a distance of the building depart from the fissure as analytical variables, in considering the dead load, live load, horizontal seismic action and combine with foundation differential settlement working conditions, analyze the elastic displacement and internal forces of the structure. The results showed that，in the topper side area near to the fissure, affected by the avoidance distance, the displacements and internal forces of the frame structure change remarkably. The growth and redistribution of internal forces performance are the most serious in the building base floor of framework， the internal forces change in ends of both beam and column will cause a change in the direction of bending moment， but also an inflection point of the column will change with the internal forces growth and regression.

Relevance. In recent years, composite materials have become widespread in the construction of reinforced concrete structures for industrial, civil and transport structures. It is proposed to strengthen the reinforced concrete structures of hydraulic structures with prestressed basalt composite rebar. It took an experimental and theoretical substantiation of technical solutions to strengthen the reinforced concrete structures of hydraulic structures with prestressed basalt composite reinforcement. The aim of the work was to carry out a set of experimental and theoretical studies of the stress-strain state and internal forces in low-reinforced concrete structures of hydraulic structures reinforced with prestressed basalt composite rebar. Methods. Experimental studies of the stress-strain state and internal forces were carried out on the basis of low-reinforced concrete beam-type models with interblock construction joints, harden with prestressed basalt composite reinforcement in the stretched (compressed) zones of the models. Theoretical studies of the stress-strain state and internal forces were carried out on the basis of the theory of reinforced concrete and structural mechanics. Results. As a result of the research carried out on typical low-reinforced concrete structures of hydraulic structures with interblock construction joints, the main stages of the stress-strain state of hydraulic reinforced concrete structures were formulated. Based on the data of experimental and theoretical studies, taking into account the reinforcement with prestressed basalt composite rebar, as well as with prestressed clamps in the shear zone, a method was developed for calculating the strength of low-reinforced hydrotechnical reinforced concrete structures with interblock construction joints.

In view of the fact that the anti sliding effect analysis of the current anchor cable and anti slide pile structure is not yet complete, research on the synergy mechanism of adjacent pile‐anchor composite structures under traffic load is carried out. Firstly, a free vibration analysis for the slope dynamic model is carried out by using a three‐dimensional finite element numerical simulation method. By improving the slope boundary conditions of time‐domain analysis, the time‐domain equation of the dynamic model of traffic load acting on the top of the slope is solved accurately, and the response law of the internal force of the pile anchor composite structure is also described. The mechanism by which the pile anchor composite structure resists against the slope sliding through the internal force increment is proposed: this internal force increment is estimated to be 73.4%, while that of anchor cable is 26.6%. The composite structure presents the coordinated sharing for sliding force. The internal force of the lower row of anchor cables is 89.48 kN larger than that of the upper row, and the internal force increment is four times larger, indicating that the lower anchor cable is more effective in slope reinforcement. As the deformation at the top of the slope is greater, the prestress of the upper anchor cable should be increased to avoid the “chain failure” caused by excessive deformation. As a result, the coordination law of internal force of pile anchor is revealed, and the anti sliding sharing mechanism is clarified. A design idea of the adjacent pile‐anchor composite structure is proposed, which takes 0.2‐0.3 times the remaining sliding force as the design value of prestressed anchor cable. The idea fully considers the anti sliding effect of prestressed anchor cables and reduces the design size of anti slide pile section, providing a theoretical support for optimization design of combined anti slide structure and saving project investment.

According to the thought of beam string structure, pre-stressing structure was presented that it was joined by rigid grid and flexible cable by pole support. It was grid string branch structure. A calculation model of string branch grid was founded. Static and dynamic characteristics of the structure that it was acted by different pre-stress value were analyzed. Through the analysis, the structure displacement and internal forces of rod are improved obviously depending on pre-stress value. The pre-stress value is larger, structure displacement and internal forces of rod are lower. Natural vibration characteristics of the structure are almost not changing, while pre-stress value is changing. When the structure is time history analysis, its response curve accords with general law of structural vibration. Node displacement response of up and bottom chord nodes are not occurred retardation effect.

In this paper the concrete-filled steel tube concrete arch bridge as the research object, through the finite element program MIDAS, analyzes the internal force of the whole bridge, determined the distribution of internal force and the most unfavorable position; Using the force balance method, taking the reasonable stress of the bending moment status to control goals, determines the boom of the bridge as the condition of reasonable internal force; Use fall down method, according to the reverse sequence in order to cut the boom, each cut as a model for internal force calculation and analysis, get the next will be cut derrick's internal force, its value is the order construction boom of the initial tension.

At present there have rarely studies on internal force and deformation for rock-socketed piles of deep excavation. The current approaches still exist and have many deficiencies and all of them didn't consider the effect of rock-socketed length. Based on the theoretical mechanics analysis of rock mass resistance, the computing methods of ultimate resistance Pult is applied to the analysis of force balance of rock-socketed part, the paper has put forward the detailed procedure for computing internal force and deformation of supporting rock-socketed piles in view of the rock-socketed length, moreover, the influence of the stability of rockmass is comprehensive considered in this method. Finally, an example is analyzed according to the procedure, the calculation results show that the method is much feasibility. The internal force and deformation of the retaining piles computed according to the procedure mentioned above satisfies the stability of rockmass.

Internal force analysis of the resistance unit of frame-truss composite wall

T his research aims to establish the limit load solution for thin-walled cylinder with circumferential crack under combined internal pressure, axial force, bending moment and torsion moment. The solution is derived based on the net-section collapse principle and the von Mises yield criterion. The material considered in this work is assumed to be elastic-perfectly plastic. The solutions obtained from this work are compared with the results from the finite element models. The comparison shows that the equations established from NSC analysis provide acceptable results for the case of cracked cylinder under combined axial force and bending moment. For the case of cylinder subjected to internal pressure or torsional moment, however, these equations can be used to predict the limit load only if np ≤ 0.40 and nT ≤ 0.6 . This is because when the effects of internal pressure or torsional moment are included, the distribution of stresses on the crack plane at the yielding does not correspond to the NSC principal.