Lecture 1-Plastic Analysis and Design

Question 1

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

Answer 1

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

Question 2

In a statically determinate beam, only one plastic hinge is required.

Answer 2

True

Question 3

M_p definition

Answer 3

Plastic moment capacity

Question 4

The plastic moment capacity M_p is…

Answer 4

The bending moment at which a plastic hinge forms.

Question 5

M_p equation

Answer 5

M_p=F_y(A/2)a = F_y*Z_x

Question 6

In plastic moment capacity equation “A” is defined as….

Answer 6

total cross sectional area

Question 7

In plastic moment capacity equation “a” is defined as….

Answer 7

the distance between centroids of the two half areas

Question 8

The factor of safety between the first yielding moment M_y can be expressed as

Answer 8

M_y=F_y*S_x

Question 9

The moment causing first yield can be written as

Answer 9

M_p/M_y = F_yZ_x/F_yS_x = Z_x/S_x

Question 10

The shape factor is

Answer 10

The constant ratio of the plastic section modulus Z_x to section modulus S_x

Question 11

For W shapes the shape factor is between

Answer 11

1.1 and 1.2

Question 12

Plastic analysis and design is covered in

Answer 12

Appendix 1 of the AISC Design by advanced analysis

Question 13

Elastic Modulus S can be found by

Answer 13

I/Y

Question 14

I (moment of inertia)

Answer 14

Moment of inertia = b*d³ / 12

Question 15

Shape Factor

Answer 15

Z/S

Question 16

The elastic section modulus S_x

Answer 16

for a given axis x-x (centroidal), describes the response of the section under elastic flexural bending, around this axis.

Question 17

The plastic section modulus, Z_x, is used to

Answer 17

determine the limit-state of steel beams, defined as the point when the entire cross section has yielded.

Question 18

For an I-section, the x-x axis, that is parallel to flanges, is typically

Answer 18

the strong axis of the cross-section

Question 19

The plastic modulus of a cross-section is given by

Answer 19

Z_x = A_cY_c + A_tY_t

Question 20

A_c*F_y

Answer 20

Represents the force on the section in compression

Question 21

A_t*F_y

Answer 21

Represents the force on the section in tension

Question 22

In the elastic section modulus “Y” represents

Answer 22

Y is the offset of a given section fiber