En222 Exam 1 Concepts

Front 1

Beam

Back 1

Any structural element that carries load primarily in bending (defined by function).
Joists (civil engineering)
Stringers (naval arch)
Carry some axial load that must be very small compared to the buckling capacity of the beam, otherwise it is a column.

Front 2

Elastic Flexture formula

Back 2

Formula which relates the beam bending moment due to loading to the stress experience by the beam fibers.
σ=(M*y)/I

Front 3

Assumptions of the Elastic Flexture formula

Back 3

1. pure bending, no vertical or horizontal shear forces
2.initially straight, constant cross-section shape
3. homogeneous, obeys Hooke's Law, material is loaded in the linear elastic range, small deflections
4. Modulus of Elasticity is the same in tension and compression

Front 4

Second Moment of Inertia

Back 4

Measure of the scatter of the area.
I=∫y^2 dA

Front 5

Section Modulus

Back 5

I/y

Front 6

Euler's Equation

Back 6

σ_crit=(π^2*E)/(L/r)^2

Front 7

Ultimate Load of a Column depends on

Back 7

1. Material Properties
2. Geometry (I, A, Depth)
3. End Conditions
4. Initial Column Eccentricity
5. Load Eccentricity

Front 8

Real Column Assumptions

Back 8

1. Initially straight and constant section area
2. Homogeneous and remains elastic (small deflections)
3. Load is applied along central axis of column
4. Pinned end conditions- no moment on end

Front 9

Equation for Biforcation point

Back 9

d^2 v/ dx^2 + Pv(x) =0

Front 10

slenderness ratio

Back 10

L/r
r is the smallest radius of gyration of the column: r=sqrt(I/A)
Buckling of a column occurs where the ratio gives the greatest value.

Front 11

Columns

Back 11

Long slender members subjected to an axial compressive force.
Buckling is the lateral deflection that occurs.

Front 12

Effective Length

Back 12

L_e = kL

Front 13

Column Design Steps

Back 13

1. Choose material, find Cc
2. Choose the orientation of the column- determine effective length (x and y), calculate kxL, kyL
The weak direction with shortest Le and strong direction with largest Le.