CVEN2303 Study Notes
Introduction
STRUCTURAL ANALYSIS
• Structural analysis can be divided into systems which are static
(stationary) or dynamic (moving)
• A structure is statically determinate if there is sufficient (equal or
greater than) equilibrium equations to unknowns
• Statically indeterminate structures can still be analysed through
introducing compatibility or material property factors
o Most structures in real-life are designed statically indeterminate to
add an additional factor of safety
o The flexibility method or stiffness method can be used to
calculate indeterminate systems
• For plane trusses and frames, it is assumed (in this course) that loads are
static, deflections are negligible and systems behave in a linearly elastic
manner
• The aim of structural analysis is to calculate internal forces and
deflections
• Engineers must plan to design a structure that is safe, aesthetic and
economical
o For a structure to be safe, it must be able to be of sufficient
strength, stability and deflection resistance
• All engineers in Australia must follow a various set of design codes, for
example the AS3600 provides guidelines for concrete structures
• Loads upon a structure can be categorized as either:
o Dead loads – weights of the permanent structural components
o Live loads – variable weights due to wind, human occupancy or
furniture
• Sign conventions are as follows:
o Upwards shear force is positive
o Bending moments inducing downwards displacement is positive
(draw the bending moment on whichever side tension occurs)
TYPES OF STRUCTURES
• A truss is a structure composed of various diagonal members connected
via hinges
o The hinges located at each node are not designed to counteract
bending moments
• Frames are composed of beams and columns via pin or fixed connections
o These are typically indeterminate structures
• Cables are flexible members that can only carry loads in tension and have
no resistance to bending or compression
• Arches are rigid structures that are designed to predominantly carry
compression loads
• Rods and bars support axial loads and can appear in many forms
including an angle (L-shape) or channel (C-shape)
, • Beams are horizontal members used to resist bending moments and
shear forces
o These can appear in a variety of cross-sections including I-section
and T-section
• Columns are vertical members used to resist axial compressive loads
o Beam-columns are required to resist bending moments as well as
vertical compressive loads
• Since an exact analysis of a real-world structure can never be made,
estimates are produced in the form of an idealised structure
• For plane trusses (2D):
o Number of unknowns = Number of Members + Number of reaction
components
o Number of equations = 2*Number of Joints
o If the number of unknowns is less than the number of equations,
the structure is unstable
CONJUGATE BEAM METHOD
• The conjugate beam method relies upon the following equations:
o Derivative of Shear Force with Distance = Shear Flow
o Second derivative of Bending Moment with Distance = Shear Flow
o Derivative of Slope with Distance = -Moment/EI
o Second derivative of Deflection with Distance = -Moment/EI
• The conjugate beam has a load equal to the Moment/EI of the real beam
• The conjugate beam has a shear force at any point equal to the slope of
the real beam
• The conjugate beam has a moment at any point equal to the vertical
deflection of the real beam
• As a result, the conjugate beam will never have a fixed support at the
same point as a fixed support on the real beam
• If the real beam is statically determinate, the conjugate beam will also be
statically determinate
• This method was originally invented in 1865 to analyse beams with
varying stiffness
PRINCIPLES OF WORK
• The total potential energy of a structure is equal to the sum of internal
strain energy and the potential energy of external loads
• Work is defined as the force applied across a displacement
• Internal strain energy is the integral of stress times strain divided by two
with respect to volume
• Castigliano’s theorem states that the internal strain energy is not
affected by the order of which loads are applied, only their final values
o The partial derivative of the strain energy with respect to
displacement is equal to the force applied at the point
• To calculate the deflection of a member due to a load, the principle of
virtual work can be used
o The internal virtual work equals the external virtual work
Introduction
STRUCTURAL ANALYSIS
• Structural analysis can be divided into systems which are static
(stationary) or dynamic (moving)
• A structure is statically determinate if there is sufficient (equal or
greater than) equilibrium equations to unknowns
• Statically indeterminate structures can still be analysed through
introducing compatibility or material property factors
o Most structures in real-life are designed statically indeterminate to
add an additional factor of safety
o The flexibility method or stiffness method can be used to
calculate indeterminate systems
• For plane trusses and frames, it is assumed (in this course) that loads are
static, deflections are negligible and systems behave in a linearly elastic
manner
• The aim of structural analysis is to calculate internal forces and
deflections
• Engineers must plan to design a structure that is safe, aesthetic and
economical
o For a structure to be safe, it must be able to be of sufficient
strength, stability and deflection resistance
• All engineers in Australia must follow a various set of design codes, for
example the AS3600 provides guidelines for concrete structures
• Loads upon a structure can be categorized as either:
o Dead loads – weights of the permanent structural components
o Live loads – variable weights due to wind, human occupancy or
furniture
• Sign conventions are as follows:
o Upwards shear force is positive
o Bending moments inducing downwards displacement is positive
(draw the bending moment on whichever side tension occurs)
TYPES OF STRUCTURES
• A truss is a structure composed of various diagonal members connected
via hinges
o The hinges located at each node are not designed to counteract
bending moments
• Frames are composed of beams and columns via pin or fixed connections
o These are typically indeterminate structures
• Cables are flexible members that can only carry loads in tension and have
no resistance to bending or compression
• Arches are rigid structures that are designed to predominantly carry
compression loads
• Rods and bars support axial loads and can appear in many forms
including an angle (L-shape) or channel (C-shape)
, • Beams are horizontal members used to resist bending moments and
shear forces
o These can appear in a variety of cross-sections including I-section
and T-section
• Columns are vertical members used to resist axial compressive loads
o Beam-columns are required to resist bending moments as well as
vertical compressive loads
• Since an exact analysis of a real-world structure can never be made,
estimates are produced in the form of an idealised structure
• For plane trusses (2D):
o Number of unknowns = Number of Members + Number of reaction
components
o Number of equations = 2*Number of Joints
o If the number of unknowns is less than the number of equations,
the structure is unstable
CONJUGATE BEAM METHOD
• The conjugate beam method relies upon the following equations:
o Derivative of Shear Force with Distance = Shear Flow
o Second derivative of Bending Moment with Distance = Shear Flow
o Derivative of Slope with Distance = -Moment/EI
o Second derivative of Deflection with Distance = -Moment/EI
• The conjugate beam has a load equal to the Moment/EI of the real beam
• The conjugate beam has a shear force at any point equal to the slope of
the real beam
• The conjugate beam has a moment at any point equal to the vertical
deflection of the real beam
• As a result, the conjugate beam will never have a fixed support at the
same point as a fixed support on the real beam
• If the real beam is statically determinate, the conjugate beam will also be
statically determinate
• This method was originally invented in 1865 to analyse beams with
varying stiffness
PRINCIPLES OF WORK
• The total potential energy of a structure is equal to the sum of internal
strain energy and the potential energy of external loads
• Work is defined as the force applied across a displacement
• Internal strain energy is the integral of stress times strain divided by two
with respect to volume
• Castigliano’s theorem states that the internal strain energy is not
affected by the order of which loads are applied, only their final values
o The partial derivative of the strain energy with respect to
displacement is equal to the force applied at the point
• To calculate the deflection of a member due to a load, the principle of
virtual work can be used
o The internal virtual work equals the external virtual work
