Force Method (25 – 54)
I. Definitions and explanations; specialties of force method and its limitations …………………………………………………………….25
II. Primary systems with replacements of static indeterminacies; choice of unknowns for force quantities and its limitations; primary system with unit forces for static indeterminacies; unit force diagrams …………2
III. Compatibility conditions and formulation of equations in matrix form, system specific matrix and its dependency upon choice of unknowns ………………………………………………………………………….29
IV. Flexibility matrix: generation and calculations ……………………..30
V. Use of graphical method for calculation of coefficients (elements of flexibility matrix); derivation of formula for the standard case of parabola and straight line, its extension to the case when both are straight lines …………………………………………………………..33
VI. Application to beams and frames; three moment theorem; effects of temperature variance and settlement of supports in beams and frames; determination of redundant reactions or member forces in a beam (two to three span) and frames (one storey two bay or two storey one bay); consideration of settlement of supports; variance in internal and external temperature for beams (up to two spans) and frames (portal only) involving not more than four unknowns…………………………….35
VII. Application to trusses; effects of temperature variance and misfits...49
VIII. Application to arches (parabolic and circular): simple cases of two hinged and hinge less arches; cases of yielding of supports and temperature effects, influence line diagrams for two hinged arches …51
I. Definitions and explanations; specialties of force method and its limitations …………………………………………………………….25
II. Primary systems with replacements of static indeterminacies; choice of unknowns for force quantities and its limitations; primary system with unit forces for static indeterminacies; unit force diagrams …………2
III. Compatibility conditions and formulation of equations in matrix form, system specific matrix and its dependency upon choice of unknowns ………………………………………………………………………….29
IV. Flexibility matrix: generation and calculations ……………………..30
V. Use of graphical method for calculation of coefficients (elements of flexibility matrix); derivation of formula for the standard case of parabola and straight line, its extension to the case when both are straight lines …………………………………………………………..33
VI. Application to beams and frames; three moment theorem; effects of temperature variance and settlement of supports in beams and frames; determination of redundant reactions or member forces in a beam (two to three span) and frames (one storey two bay or two storey one bay); consideration of settlement of supports; variance in internal and external temperature for beams (up to two spans) and frames (portal only) involving not more than four unknowns…………………………….35
VII. Application to trusses; effects of temperature variance and misfits...49
VIII. Application to arches (parabolic and circular): simple cases of two hinged and hinge less arches; cases of yielding of supports and temperature effects, influence line diagrams for two hinged arches …51