Lecture 1-Plastic Analysis and Design Flashcards
T/F Failure of a structure will take place at a load that forms enough plastic hinges to create a mechanism that will undergo contained displacement with an increase in load
False: Failure of a structure will take place at a load that forms enough plastic hinges to create a mechanism that will undergo uncontained displacement without an increase in load
In a statically determinate beam, only one plastic hinge is required.
True
Mp definition
Plastic moment capacity
The plastic moment capacity Mp is…
The bending moment at which a plastic hinge forms.
Mp equation
Mp=Fy(A/2)a = Fy*Zx
In plastic moment capacity equation “A” is defined as….
total cross sectional area
In plastic moment capacity equation “a” is defined as….
the distance between centroids of the two half areas
The factor of safety between the first yielding moment My can be expressed as
My=Fy*Sx
The moment causing first yield can be written as
Mp/My = FyZx/FySx = Zx/Sx
The shape factor is
The constant ratio of the plastic section modulus Zx to section modulus Sx
For W shapes the shape factor is between
1.1 and 1.2
Plastic analysis and design is covered in
Appendix 1 of the AISC Design by advanced analysis
Elastic Modulus S can be found by
I/Y
I (moment of inertia)
Moment of inertia = b*d3 / 12
Shape Factor
Z/S
The elastic section modulus Sx
for a given axis x-x (centroidal), describes the response of the section under elastic flexural bending, around this axis.
The plastic section modulus, Zx, is used to
determine the limit-state of steel beams, defined as the point when the entire cross section has yielded.
For an I-section, the x-x axis, that is parallel to flanges, is typically
the strong axis of the cross-section
The plastic modulus of a cross-section is given by
Zx = AcYc + AtYt
Ac*Fy
Represents the force on the section in compression
At*Fy
Represents the force on the section in tension
In the elastic section modulus “Y” represents
Y is the offset of a given section fiber
