Bending Stiffness Values Research Articles

Influence of rope fastening on the spectrum of its natural transverse vibrations

According to the previously developed method, which takes into account the bending stiffness of steel ropes during their transverse oscillation, the ropes of the pedestrian bridge ‘Lovers’ in the city of Tyumen were investigated. The obtained values of tension forces and bending stiffness were within the expected range. The high variation of bending stiffness values forced to pay attention to the accuracy of the initial values of rope lengths, which were obtained from the photograph. To measure the rope lengths, a method of nodal harmonic registration was proposed, but the results obtained by this method were higher than the values obtained from the photograph. The evaluation of measurement errors did not explain this overestimation, which led to the necessity to revise the solution of the differential equation of transverse oscillations. It turned out that previously only its partial solution was considered, assuming a hinged rope attachment, whereas it is cantilevered and has a bending reaction. Taking this feature into account by introducing an additional boundary condition allowed to improve the calculation model and explain the overestimation of the rope length in the method of nodal harmonics.Taking into account the nature of the rope attachment allowed us to introduce a generalised parameter s, which takes zero value for rigid cantilever attachment, and is equal to one for articulated attachment. Then the stiffness weakening inside the anchorage will be manifested by the growth of the parameter s and can be detected by the results of the oscillation spectrum registration.

Extension of paperboard modelling with Föppl–von Karman terms for improved stress state under suction pressure

A practical method for solving the bending stiffness of a thin orthotropic plate based on measured deflection and known loading was studied. The target application was paperboard manufacturing and related process control. Here, finite element (FE) method was used to create virtual paperboard and its deflection data. The accuracy of the linear Kirchhoff plate model used in the practical method was tested against the FE model with known load and material properties. It was found that in the case of significant deflections, the linear Kirchoff model was not accurate. The non-linear Föppl--von Kàrmàn model takes into account the occurring membrane stresses and extends on the Kirchhoff model, allowing for larger deflection. The non-linear Föppl--von Kàrmàn model was found to successfully describe the simulated situation and could be used to better solve for the paperboard's bending stiffness values over two axes.

Evaluation of bending and shear properties of mixed softwood & hardwood cross-laminated timbers

The current version of PRG-320 Standard for Performance-Rated Cross-Laminated Timber (CLT) that governs CLT manufacturing and design, limits production to softwood species. As a result, the growing demand for CLT production could strain the supply of softwood lumber in the US within the next decade. The inclusion of hardwood in CLT production alongside softwood could be a potential solution to this problem. This paper investigates the bending and shear test results of three- and five-layer mixed species CLT beams manufactured using various combinations of yellow-poplar and southern pine. The beams were evaluated for bending strength, bending stiffness, shear strength, and shear stiffness, as well as quality control testing of moisture content, specific gravity, resistance to shear by compression loading and resistance to delamination. The experimental values for all CLT groups, adjusted according to the Allowable Stress Design (ASD) to ensure stress limits are not exceeded, were greater than those calculated using the shear analogy method. The only exceptions were bending stiffness values for the groups with all layers of southern pine and those with outer layers of southern pine and inner layers of yellow-poplar (see Table 1 for layups codes), where the differences remained within a minor range of 4 %. Although, wood failure percentages in resistance to shear by compression loading fell below the maximum value of 80 %, and face delamination percentages in resistance to delamination were above the minimum value of 5 % according to the corresponding standards. The mechanical properties of all CLT beams met or exceeded shear analogy values. The test results indicated that yellow-poplar could be a viable alternative to southern pine in the production of CLT due to its similar specific gravity. This suggests that mixed-species CLT can maintain or enhance structural performance while addressing material shortages. Furthermore, the use of yellow-poplar in CLT production promotes sustainable forestry practices, supports resource diversification, and encourages innovation in construction methods. These findings have significant practical implications for the timber and construction industries, contributing to cost efficiency and environmental sustainability.

Simulation and parameterization of nonlinear elastic behavior of cables

AbstractThis work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

Developing a lightweight corrugated sandwich panel based on tea oil camellia shell: correlation of experimental and numerical performance

This study presents an experimental and numerical comparison between the mechanical performance of a lightweight corrugated sandwich panel based on the tea oil camellia shell (TOCS). Hence, TOCS was mixed in two groups with Poplar particles and fibers. After that, in the experimental part, the conventional mechanical tests, including the 3-point bending test, flatwise compression, dowel bearing, and screw resistance, and in the numerical part, finite element analysis (FEA), including the normal, maximum principal, and equivalent (von Mises) stress by Ansys Mechanical software carried out. The specimens for experimental and numerical tests were prepared in transverse and longitudinal directions. Before that, the engineering data (shear modulus, Young's modulus, and Poisson's ratio) for improving the FEA simulation were obtained from TOCS-based flat panels fabricated with a mixture of Poplar particles and fibers. The results of FEA are used to compare the mechanical behavior and failure mechanism with the results of experimental tests. According to the mean values of bending stiffness and maximum bending moment, sandwich panels made with 100% particles demonstrated an advantage in both directions. Nevertheless, the compression strength and screw resistance showed the same trend, but the dowel bearing showed higher values for panels made with fibers. The observed results of equivalent (von Mises) stress indicated a coloration with the results of failure mechanisms.

Numerical Analysis of Laminated Veneer Lumber Beams Strengthened with Various Carbon Composites.

Among the many benefits of implementing numerical analysis on real objects, economic and environmental considerations are likely the most important ones. Nonetheless, it is also crucial to constrain the duration and space necessary for conducting experimental investigations. Although these benefits are clear, the applicability of such models must be appropriately verified. This research subjected validation of numerical models depicting the behavior of unstrengthened and strengthened laminated veneer lumber (LVL) beams. As a reinforcement, a carbon fiber reinforced polymer (CFRP) sheet and laminates were used. Experiments were conducted on full-scale members within the framework of the so-called four-point bending testing method. Numerical simulations were performed using the Abaqus software. Two types of material models were examined for laminated veneer lumber: linearly elastic and linearly elastic-perfectly plastic with Hill's yield criterion. A distinction was made in the material properties of carbon composites based on their location on the height of the cross-section. The outlined numerical models accurately depict the behavior of real structural elements. The precision of predicting load-bearing capacity amounts to a few percent for strengthened beams and a maximum of eleven percent for unstrengthened beams. The relative deviation between numerical and experimental values of bending stiffness was at a maximum of seven percent. Applying the elastic-plastic model enables accurate representation of the load versus deflection relation and the distribution of stress and deformation of strengthened beams. Based on the findings, directives were provided for further optimization of the positioning of composite reinforcement along the span of the beam. Reinforcement design of existing laminated veneer lumber members can be made using presented methodology.

Topology optimization based on combined mechanical analysis and variable density method for casting structure

In this study, a topology optimization method based on combined mechanical analysis and variable density is presented for a large-scale casting structure with complex thin-walled structures. First, the mechanical analysis model of the frame is established, the first-order bending and torsional modes and stiffness values of the all-cast aluminum frame are obtained, and the basic mechanical parameters such as bending/torsional mode and stiffness constraints needed for topology optimization are defined. Using the variable density method, unneeded material that can be removed from the casting structure is identified. According to the design requirements, the optimization objective function and constraint conditions are established, and the variable density method is used to solve the problem. Analysis of the mechanical results before and after topology optimization reveals that the modes and stiffness values are larger than the target values, and the mass of the frame is reduced by 10.2 kg (i.e. 13.9%) compared with the original design. The application of the combined mechanical analysis and variable density method to a casting structure can effectively achieve lightweight design.

Model of influence of a rope defect on the spectrum of its free transverse vibrations

In earlier work the possibility of diagnosing a defect of a steel wire rope by spectral composition of its free transverse vibrations was substantiated. In the present work, an analytical model of transverse vibrations of a steel wire rope with local damage is proposed. The presence of the defect in the model is taken into account only in the form of a loss of bending stiffness of the corresponding section without changing the specific mass along the length. The model represents three homogeneous rope sections “stitched” together, where the middle one represents a defective section with a lower value of bending stiffness. According to the model calculations, it is shown that the character of the dependence of the natural frequencies of oscillations on their number practically does not change in the presence of a defect. However, its presence and location affects the ratio of vibration amplitudes of undamaged sections, which can be used to monitor the condition of the rope.

Flow resistance due to shrubs and woody vegetation

In this paper, a theoretical open channel flow resistance equation was verified using flow depth and discharge measurements carried out by Freeman et al. in a large channel, 2.44 m wide, for ten different types of uniform-sized plants (shrubs and woody vegetation). The plants, which are broadleaf deciduous vegetation commonly found in floodplains and riparian zones, were placed in staggered rows inside the channel whose bed was constructed to accept plants with their root systems. For each species, the available measurements were carried out by Freeman et al. with plants having different values of plant density, height, and bending stiffness. The available literature database (87 measurements) was divided into two groups which were separately used to calibrate and test the theoretical approach. In particular, 46 measurements were used to calibrate the relationship between the scale factor Γ of the velocity profile, the Froude number, and the channel slope. This relationship was calibrated using the entire available dataset or varying the scaling coefficient a with the investigated vegetation type. The measured values of the Darcy-Weisbach friction factor, obtained by the measured flow velocity, water depth and slope values, were compared with those calculated by the theoretical flow resistance law, coupled with the relationship for estimating the Γ function having a scaling coefficient different for each investigated vegetation type. This comparison allowed to demonstrate that an accurate estimate of the Darcy-Weisbach friction factor (errors less than or equal to ±10% for 87% of the investigated cases) can be obtained. However, for the investigated vegetation species, that are characterized by a large range of bending stiffness, also a mean value of the scaling coefficient a equal to 0.3283 allows an accurate estimate of the Darcy-Weisbach friction factor.

Out-of-plane strengthening of URM walls using different fiber-reinforced materials

Fiber-reinforced polymers (FRPs), textile-reinforced mortars (TRMs), and engineered cementitious composites (ECCs) have been extensively employed to address the insufficient load-carrying capacity and low deformation capability of unreinforced masonry buildings. In this study, eight groups of unreinforced masonry walls were built to test the efficiencies of various reinforcing methods under out-of-plane four-point loading. A high-strength mortar reinforcement were employed as benchmarks. Four types of ECCs—low-cost, high-strength, lightweight insulation, and high-toughness ECCs—were compared with carbon FRP (CFRP) sheet and TRM systems. The failure modes, midspan load–displacement actions, energy absorption capabilities, initial bending stiffness values, and ductility of the different reinforcement systems were obtained and analyzed. The results revealed that the TRM-reinforced specimens experienced the maximum midspan deformation. The best ductility and maximum bearing capacity were obtained respectively after reinforcements with high-strength and high-toughness ECCs. However, the exploitation of the CFRP sheet was limited owing to excessive reinforcement. Finally, the moment capacity was evaluated using a flexural model. For the specimens that failed in the shear mode, a shear model based on the equilibrium condition was established to predict their load-carrying capacities.

Strengthening of Full-Scale Laminated Veneer Lumber Beams with CFRP Sheets.

This paper presents the results of experimental research on full-size laminated veneer lumber (LVL) beams unreinforced and reinforced with CFRP sheets. The nominal dimensions of the tested beams were 45 mm × 200 mm × 3400 mm. The beams were reinforced using the so-called U-type reinforcement in three configurations, differing from each other in the thickness of the reinforcement and the side surface coverage. An epoxy resin adhesive was used to bond all the components together. A four-point static bending test was performed according to the guidelines in the relevant European standards. The effectiveness of the reinforcement increased with the level of coverage of the side surface and the level of reinforcement. The average increases of bending resistance were 42%, 51% and 58% for configurations B, C and D, respectively. The average value of bending stiffness increased for the beams of series B, C and D by 15%, 31% and 43%, respectively. Their failure mode changed from brittle fracture initiated in the tensile zone for unreinforced beams to more ductile fracture, initiated in the compression zone. The influence of the coverage of the side surface by the CFRP sheet and reinforcement ratio on the mechanism of failure and effectiveness of strengthening was studied in the article.

The evaluation of a de novo biplanar distal humerus plate: A biomechanical study.

Objectives The aim of this study was to compare the stability of a novel biplanar distal humerus plate with the single- and doublecolumns J-plating techniques.Materials and methods Eighteen sawbones humera were divided into three groups. In Groups 1, 2 and 3, biplanar plate, single lateral J-plate and double J-plate, were used, respectively. Transverse osteotomies at the upper portion of the olecranon fossa were made. Blocks of 10-mm was removed from each sample. Axial, torsional, and extensional stiffness of each group were measured.Results The mean axial stiffness values in Groups 1, 2, and 3 were 64.80±6.75, 33.70±5.71, and 171.48±9.53 N/mm, respectively. Group 1 demonstrated a statistically significant difference compared to Group 2 (p=0.032), whereas Group 3 showed a statistically significant difference compared to Groups 1 and 2 (p=0.025 and p=0.014, respectively). The mean torsional stiffness values of Groups 1, 2, and 3 were 0.23±0.01, 0.14±0.008, and 0.30±0.007 N/ degree, respectively. Groups 1 and 3 demonstrated a statistically significant difference compared to Group 2 (p=0.042 and p=0.028, respectively). No statistically significant difference was detected between Groups 1 and 3 (p=0.27). The mean extensional bending stiffness values of Groups 1, 2 and 3 were 2.64±0.31, 1.17±0.13, and 3.2±0.1 N/mm, respectively. Group 1 demonstrated a statistically significant difference compared to Group 2 (p=0.041). There was no statistically significant difference between Groups 1 and 3 (p=0.083).Conclusion Biplanar plate allows applying enough numbers of long sagittal screws and offers more biomechanical stability than lateral column J-plate and in some aspects strong as dual J-plating in torsional and bending tests.

Effect of Layer Arrangement on Bending Strength of Cross-Laminated Timber (CLT) Manufactured from Poplar (Populus deltoides L.)

This study aimed to investigate the effect of layer arrangement on bending properties of CLT panels made from poplar (Populus deltoides L.). A total of 20 three-layer CLT panels with the same dimensions of 1300 × 360 × 48 mm3 (Length, Width, Thickness) were fabricated in five configurations: 0/30/0, 0/45/0, 0/90/0, 45/0/45, and 45/45/45. The apparent modulus of elasticity (MOEapp), modulus of rupture (MOR) and apparent bending stiffness (EIapp) values in major and minor axes of CLT panels were calculated using experimental bending testing. In the major axis, the highest values of MOR, MOEapp, and EIapp were obtained from the 0/30/0 arrangement, while the least values resulted from the arrangements of 90/60/90 and 90/45/90 in the minor axis. Besides, in all arrangements, the average of the experimental apparent bending stiffness values (EIapp,exp) of specimens was higher than that of the shear analogy apparent bending stiffness values (EIapp,shear). The bending and shear stress distribution values over the cross section of samples were also estimated using the finite element method. Moreover, the numerical apparent bending stiffness (EIapp,fem) values of samples were compared to experimental apparent bending stiffness (EIapp,exp) values. Based on experimental and finite element method results, in all groups of layer arrangements, the EIapp,fem values concurred well with the EIapp,exp values.

Comparison of three methods for measuring the bending stiffness of ultrafine metal wires

Abstract Ultrafine metal wires have been widely used as structural constituents of metal meshes for electromagnetic interference shielding. To investigate the bending property of metal wires during the knitting process, the three-point bending, cantilever bending, and pure horizontal bending methods were carried out and compared. The relationships among the bending property, the twist pitch and the number of twisted wire strings were also analyzed. The specific dependence of the bending stiffness on twist pitch resulted from the internal frictional constraints, and a twist pitch of 4.5 mm was chosen as the optimized twisted parameter. The bending properties evaluated by the three methods were equally sensitive to the twist pitch, and a similar linear trend of bending stiffness with the number of twisted wire strings was found. The values of bending stiffness from the three methods were significantly different, and the descending order was the three-point bending, the cantilever bending, and the pure horizontal bending method. The correlation coefficient of the three methods was higher than 0.935, which is a strong positive correlation. From the investigation came a conclusion that the three-point bending method is more useful in realistic conditions because of its diversity and universality for various bending deformations.

Investigation into Mechanical Properties and Failure Mechanisms of Novel Sandwich Composite Material with Carbon Fibre / Epoxy Facesheets and PVC Foam Core

Sandwich composite materials have seen a significant increase in use across various engineering fields and applications due to their exceptional mechanical properties, including high specific strength and bending stiffness values. Because of their high strength properties, the use of sandwich structures is preferred in different industries. It is crucial to investigate material properties of novel composites in order to estimate their failure mechanisms under different loading types. In this study, a type of sandwich composite material consisting of Carbon Fibre/Epoxy Facesheets with two different dimensions and a PVC Foam Core was designed and fabricated. The selection of PVC foam for this study is motivated by its wide use in load bearing components in different industries. The sandwich composite material used for the experiments was manufactured by using vacuum-assisted resin infusion moulding process (VARIM) by IZOREEL in Izmir, Turkey. Failure styles of the structure in compression, shearing and bending were revealed by sandwich flatwise tension, core flatwise compression, and sandwich edgewise compression tests. Facesheet bending of manufactured composites have been investigated experimentally. Tensile strength of the facesheets and sandwich material have been presented separately. The detailed formulations and procedures are provided. The obtained results are discussed, and it is seen that maximum tensile and compression stresses in the three-point bending test depend on the direction of the loading with respect to different facesheet thicknesses.

CLT Fabricated with Gmelina arborea and Tectona grandis Wood from Fast-Growth Forest Plantations: Physical and Mechanical Properties

Fabrication and use of Cross Laminated Timber (CLT) using tropical woods is still limited at present. Therefore objective of the present study aims to determine the possibility of using CLT panels of 3 and 5 layers, fabricated with Tectona grandis and Gmelina arborea wood using adhesive of isocyanate polymer emulsion system catalyzed with polymeric isocyanate. Delamination, water absorption, density, flexure test, compression and glue-line shear were evaluated using ANSI/APA PRG320-2012 ASTM D198 and ASTM D4761 standard. The results showed that CLT panels of T. grandis presented higher values of density, less water absorption and lower delamination, with no evident differences between the CLT of 3 and 5 layers. The high density of T. grandis resulted in higher values of the mechanical properties. The flatwise and edgewise flexure tests in 5-layer CLT panels of both species presented higher values of bending stiffness compared to those of 3-layer CLT panels. Further the bending stress values in 3-layer CLT panels were higher than for 5-layer CLT panels. As for shear stress in bending flatwise, in both species, 3-layer CLT surpassed 5-layer CLT panels, but in the edgewise test no differences were observed. The MOE and Fc in the compression test were superior in relation to the edgewise test. MOE and Fc in compression flatwise in 3-layer CLT was greater than in 5-layer CLT in both species, but edgewise these values were higher in 5-layer CLT panels. The most common failures were stress and delamination in the flexure test, whereas in the compression test these were: shearing, splitting and crushing. In the glue-line shear test no differences were observed between CLT panels of 3 and 5 layers for both species.

Structural Application of Lightweight Panels Made of Waste Cardboard and Beech Veneer.

In recent years, the furniture design trends include ensuring ergonomic standards, development of new environmentally friendly materials, optimised use of natural resources, and sustainably increased conversion of waste into value-added products. The circular economy principles require the reuse, recycling or upcycling of materials. The potential of reusing waste corrugated cardboard to produce new lightweight boards suitable for furniture and interior applications was investigated in this work. Two types of multi-layered panels were manufactured in the laboratory from corrugated cardboard and beech veneer, bonded with urea-formaldehyde (UF) resin. Seven types of end corner joints of the created lightweight furniture panels and three conventional honeycomb panels were tested. Bending moments and stiffness coefficients in the compression test were evaluated. The bending strength values of the joints made of waste cardboard and beech veneer exhibited the required strength for application in furniture constructions or as interior elements. The joints made of multi-layer panels with a thickness of 51 mm, joined by dowels, demonstrated the highest bending strength and stiffness values (33.22 N∙m). The joints made of 21 mm thick multi-layer panels and connected with Confirmat had satisfactory bending strength values (10.53 N∙m) and Minifix had the lowest strength values (6.15 N∙m). The highest stiffness values (327 N∙m/rad) were determined for the 50 mm thick cardboard honeycomb panels connected by plastic corner connector and special screw Varianta, and the lowest values for the joints made of 21 mm thick multi-layer panels connected by Confirmat (40 N∙m/rad) and Minifix (43 N∙m/rad), respectively. The application of waste corrugated cardboard as a structural material for furniture and interiors can be improved by further investigations.

Experimental study on bending properties of cross-laminated timber-bamboo composites

Using bamboo and timber to manufacture cross-laminated timber-bamboo (CLTB) composites could utilize the advantages of two material to improve the mechanical properties and expand the raw material source of cross-laminated timber (CLT). To explore the feasibility of using engineered bamboo as CLT lamination, the rolling shear properties of two bamboo scrimbers and one bamboo plywood were evaluated. Two types of CLTB specimens, using bamboo scrimber as transverse layer or as both transverse layer and the outermost longitudinal layer, were developed in this study. The bending properties of CLTB and generic Spruce-pine-fir (SPF) CLT specimens were evaluated by dynamic tests and third-point bending tests, respectively. The shear analogy method was employed to calculate the apparent bending stiffness of CLT/CLTB specimen. The results indicated that the rolling shear modulus and strength of bamboo scrimber (group RB(F)-4.5) were 92.81% and 98.64% higher than those of bamboo plywood, respectively, and were 330.19% and 121.13% higher than those of SPF dimension lumber, respectively. The CLTB specimens, group BWBWB, had 23.69% and 60.50% higher apparent bending modulus and peak load than those of generic SPF CLT specimens. Most of the CLTB bending specimens had main failure mode of tensile failure in the bottom layer which replaced rolling shear failure in transverse bamboo scrimber layer. The apparent bending stiffness values of CLT/CLTB specimens obtained from dynamic test and shear analogy method were in good agreement with the static experimental values. The results presented in this paper can provide fundamental basis for supporting the potential engineering application of CLT panel products fabricated with bamboo scrimber.

A Study on the Bending Stiffness of a New DNA Origami Nano-Joint.

The present article aims to investigate the mechanical properties of a new DNA origami nano-joint using the steered molecular dynamics (SMD) simulation. Since the analysis of mechanical properties is of great importance in bending conditions for a nano-joint, the forces are selected to achieve angular changes in the joint by the resultant torque. In this study, the nano-joint is considered as a beam in order to use mechanical equations to extract the mechanical properties of the designed nano-joint. In addition, the bending stiffness of the beam is investigated in different modes of deflection using the Euler-Bernoulli beam theory. The results revealed that the value of bending stiffness increases with increasing deflection, and the changes in the bending stiffness relative to the deflection is linear. The proposed DNA origami nano-joint can be used as a joint in nanorobots and can be effectively applied in nanorobotic systems to move different components.

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

In current structural analyses on segmental linings, the bending stiffness of segmental joints is usually treated as a constant, which results in a deviation in the calculated internal forces and deformation. In view of this, a finite element model of segmental linings is established using one ring and two half rings. An iterative algorithm is designed with a 3D curved surface of bending stiffness for the segmental joint, obtained from a series of full-scale tests under different axial force and bending moment cases. The rational convergence criteria for the iterative algorithm are recommended by evaluating the convergence efficiency of the iterative algorithm. Moreover, the influence of load magnitude and initial value of bending stiffness, as well as the changing laws of structural internal forces and deformation with the assembly angles, are presented and analyzed. The results show that with the same load, the convergence of the iterative algorithm in staggered-jointed assembly structures (STGS) is better than that of straight-jointed assembly structures (STRS), owing to its greater overall stiffness. The initial input value of bending stiffness has no effect on the convergence of the proposed iterative algorithm, and generally the convergence performance in STGS is better than that in STRS. In STRS, the bending moment is most sensitive to the changes of assembly angles, while in STGS the assembly angles have great influence on both the bending moment and structural displacement. Without the stiffness iteration, the maximum differences for maximum axial force, bending moment, and displacement under different assembly angle in STRS are 11.7%, 31.9% and 22.3%, respectively, and that differences in STGS are 10.4%, 59.3% and 35.1%, respectively. With the stiffness iterative method, the increase amplitude of the maximum axial force, the maximum bending moment, and the maximum displacement in STRS and STGS are 50.0%, 317.4%, 77.1% and 41.9%, 459.3%, 156.5%, respectively, indicating that changing the assembly angles is a rational way to control the internal structural forces and deformations.