Graph Algorithm For Carrying Capacity Anddeformation Of Normal Section Of Concrete Members

The calculation of reinforcement for concrete structures is based on the Code for Design of Concrete Structures GB50010-2010.The equivalent rectangular stress conversion is used to calculate the bearing capacity of the normal section of flexural members with rectangular or circular cross sections.However,the rectangular stress conversion of the bearing capacity of the circular section members will bring a lot of errors.Moreover,the calculation of bearing capacity of circular section has double nonlinearity(variation of material and section width).The bearing capacity of the circular section can only be calculated iteratively through the transcendental equations in Appendix E of the specification.There are three nonlinear factors(material,geometry and section width change)in the bearing capacity calculation of special circular section members considering the second-order effect,which is inconvenient for calculation.When calculating the reinforcement of concrete members,the yield strength of reinforcement should be used,but the tensile strength of the small eccentric axial compression members or the stress of the reinforcement of the small compression members may not reach the yield strength,which makes the calculated results unsafe.The crack width on the structural member will affect the suitability and durability of the member,after the calculation of bearing capacity,the crack width of the member should be checked,but the checking procedure is complicated.In order to simplify or solve the impact of the above problems,this paper mainly does the following work:1.Calculate the actual stress distribution on the rectangular and circular sections according to the strain distribution on the section of the member,and then calculate the internal force on the section of the member and judge the stress state of the member.2.Based on the actual stress distribution on circular sections,a method for calculating the bearing capacity of circular and circular sections of concrete without iteration is derived and calculated.3.A chart which can be used for calculating the non-uniform reinforcement of concrete circular and annular section members is derived and drawn.4.A chart which can be used for the calculation of symmetric reinforcement of rectangular and I-shaped section members is derived and drawn.5.The increase coefficient method in consideration of the second-order effect calculation in the Specification is introduced into the reinforcement calculation chart,and the reinforcement calculation chart of the rectangular,I-shaped and circular crosssection members considering the second-order effect is drawn.6.The calculation method and principle of crack width are introduced.According to the formula of maximum crack width in the Code,the maximum diameter of reinforcement without checking the crack width is derived.7.The correlation curve between reinforcement diameter and reinforcement ratio of the member is derived and plotted.The crack width of the member can be judged to meet the limit value by the diameter of reinforcement in the member.