Columns + Kinematics and Stresses

Question 1

Slenderness Ratio

Accepted Answer

$SR=\frac{L_e}{k}$ effective length / radius of gyration

Question 2

Radius of Gyration

Accepted Answer

$k=\sqrt{\frac{I}{A}}

Question 3

Effective Length

Accepted Answer

$L_e=KL

Question 4

Normal Stress

Accepted Answer

$S=\frac{F}{A}

Question 5

Factor of Safety

Accepted Answer

$FS=\frac{S_{ultimate}}{S_{design}}

Question 6

Normal Stress w/ D and d

Accepted Answer

$S=\frac{F}{\frac{π}{4}(D^2-d^2)}

Question 7

Thickness

Accepted Answer

$t=\frac{D-d}{2}$ $t=r_o-r_i

Question 8

Shear Stress

Accepted Answer

$S=\frac{F}{πDt}

Question 9

Bolt Stress

Accepted Answer

$S_{bolt}=\frac{\frac{PA_{cylinder}}{N_{bolts}}}{A_{bolt}}

Question 10

Modulus of Elasticity of Steel

Accepted Answer

$E_{steel}=30x10^6 psi

Question 11

Modulus of Elasticity of Aluminum$

Accepted Answer

$E_{Al}=\frac{1}{3}E_{steel}

Question 12

Modulus of Rigidity of Steel

Accepted Answer

$G=12x10^6psi

Question 13

Poissons Ratio and 2big

Accepted Answer

$v=-\frac{Ɛ_{lateral}}{Ɛ_{longitudinal}}$ $E=2(v+1)G

Question 14

Axial Deformation

Accepted Answer

$δ=\frac{FL}{AE}

Question 15

Elongation

Accepted Answer

$Ɛ=\frac{δ}{L}

Question 16

Deformation Due to Own Weight

Accepted Answer

$δ=\frac{ρgL^2}{2E}

Question 17

Dilatation

Accepted Answer

$e=Ɛ_x+Ɛ_y+Ɛ_z$ $e=\frac{F}{AE}(1-2v)

Question 18

Thermal Elongation and Thermal Stress

Accepted Answer

$δ=αL∆T$ $S=Eα∆T$ $\alpha=6.51x10^{-6}°

Question 19

Bending/Flexural Stress

Accepted Answer

$S_b=\frac{Mc}{I_x}

Question 20

Flexural/Bending Stress Square Cantilever Beam

Accepted Answer

$S_b=\frac{6M}{bh²}

Question 21

Flexural/Bending Stress Circular Cantilever

Accepted Answer

$S_b=\frac{32M}{πD³}

Question 22

Maximum Moment 2 formulas

Accepted Answer

$M_{max}=\frac{ωL^2}{8}$ $M_{max}=\frac{PL}{4}

Question 23

Band Saw

Accepted Answer

$S=\frac{Et}{D}

Question 24

Slenderness Ratio

Accepted Answer

$SR=\frac{L_e}{k}

Question 25

Effective Length and End Coefficient

Accepted Answer

$L_e=KL$ $C=\frac{1}{K^2}

Question 26

Max Moment

Accepted Answer

$M_{max}=\frac{PL}{4}$ $M_{max}=\frac{\omega L^2}{8}

Question 27

Moment of Inertia Square

Accepted Answer

$I_x=\frac{bh^3}{12}

Question 28

Moment of Inertia Triangle

Accepted Answer

$I_x=\frac{bh^3}{36}

Question 29

Moment of Inertia Circle

Accepted Answer

$I_x=\frac{\pi r^4}{4}$ $I_x=\frac{\pi D^4}{64}

Question 30

Radius of Gyration

Accepted Answer

$k=\sqrt{\frac{I}{A}}

Question 31

Buckling Formula: Euler's

Accepted Answer

$F_c=\frac{π^2EI}{L_e^2}

Question 32

Buckling Formula: JB Johnson

Accepted Answer

$F_c=S_yA\left[1-\frac{S_y(L_e/k)^2}{4π^2E}ight]

Question 33

Maximum Shear Stress (Combined Stresses)

Accepted Answer

$Ss_{max}=\sqrt{\left(\frac{S_x-S_y}{2}ight)^2+S_s^2}

Question 34

Maximum Stress (Combined)

Accepted Answer

$S_{max}=\frac{S_x+S_y}{2}+Ss_{max}

Question 35

Minimum Stress (Combined)

Accepted Answer

$S_{min}=\frac{S_x+S_y}{2}-Ss_{max}

Question 36

Degree of Freedom

Accepted Answer

$DOF=3(N-1)-2L_{pair}-H_{pair}$ $DOF=3(N-1)-2L_{pair}

Question 37

Alternating Stress

Accepted Answer

$S_a=\frac{S_x-S_y}{2}

Question 38

Mean Stress

Accepted Answer

$S_m=\frac{S_x+S_y}{2}

Question 39

For Static Failure, FS 2 formulas

Accepted Answer

$FS=\frac{S_y}{S_m}$ $FS=\frac{S_u}{S_m}

Question 40

Instantaneous Center

Accepted Answer

$v=r\omega$ $\omega=\frac{v_A}{r_A}=\frac{v_B}{r_B}

Columns + Kinematics and Stresses

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