Plastic theory introduction

Question 1

What is elastic design?

Answer 1

Applied load<Yield point

Question 2

What is plastic design?

Answer 2

Applied load<Collapse

Question 3

Where is plastic design used?

Answer 3

Used in steel structure as they undergo plastic deformation before they fail completely

Question 4

How can linear elastic behaviour be characterized?

Answer 4

• Small laods
• Stress<yield stress
• Linear stress-strain behaviour
• Small and recoverable

Question 5

How can plastic behaviour be characterized?

Answer 5

• Extreme loads
• Stress > yield stress
• Non-linear stress-strain behavior
• Large and permanent deformations
• Ultimate failure

Question 6

What do we assume about materials that deform?

Answer 6

• Is assumed to behave as a perfectly plastic
• Ignore strain hardening and necking

Question 7

What increases as stress remains constant?

Answer 7

Strain

Question 8

What is the equation for bending moment at first yield?

Answer 8

M_y=σ_yI/y_m

Question 9

What is the max bending moment?

Answer 9

PLASTIC MOMENT (M_p)

Question 10

What are the 3 phases of a material?

Answer 10

• Linear elastic
• Partially plastic
• Fully plastic

Question 11

What does plastic analysis allow us to do?

Answer 11

• Determine the ultimate load at failure
• Determine the true safety factor against failure
• Achieve economical design

Question 12

What is the plastic moment?

Answer 12

The sum of all the compressive and tensile moments

Question 13

When does the elastic neutral axis equal the plastic neutral axis?

Answer 13

When the beam is symmetrical

Question 14

How can plastic section modulus be calculated?

Answer 14

Z_p=I/y_m = M_p/σ_y

Question 15

What is the shape factor?

Answer 15

Ratio of the plastic moment to the moment at first yield

Question 16

What is the shape factor for a standard I beam?

Answer 16

~ 1.15

Question 17

How can the shape factor be calculated?

Answer 17

α=M_p/M_y