Steel Design

Two types of Connection

1. Bolted

2. Welded

Tension Based on Gross Area of Plate

$f_{t}=\frac{P}{A_{g}};f_{t}=0.6F_{y}$ (ASD Factor of Safety = 1.67)

$$P=0.6F_{y}A_{g}$$

Tension Based on Net Rupture

$$f_{t}=\frac{P}{A_{n}};f_{t}=0.5F_{u}$$

$$P=0.5F_{u}A_{e}$$

Bearing Failure of Plates (LRFD)

$$f_{p}=\frac{P}{A};f_{p}=1,2F_{u}$$

$$T=1.2F_{u}A_{p}$$

Deformation at Bolt Hole and Tear Out Failure (ASD)

$$R_{n}=2.4\cdot d\cdot t\cdot F_{u}$$

$$R_{n}=1.2\cdot L_{c}\cdot t\cdot F_{u}$$

Allowable Tensile Stresses

Relationship of Reduction Factor and Factor of Safety

$$\frac{1.5}{\phi}=\Omega_{t}$$

Effective Net Area

$A_{e}=$ lesser of:

(1) $0.85A_{g}$

(2) $UA_{n}$

Where U → Shear Lag Factor

Shear Lag Factor, U

For Plates: 1.0

For Angles:

$$U=1-\frac{\overline{x}}{L}$$

L = Length of Connection

Cochrane’s Equation for Staggered Bolts

$$A_{net}+\frac{s^2}{4g}$$

Where S (stagger or pitch) = Horizontal Distance

g (gage) = Vertical Distance

Block Shear Strength

$$P=0.5F_{u}A_{t}+0.3F_{u}A_{v}$$

Out of Plane Eccentric Load

Causes Bending

In-Plane Eccentric Load

Causes Torsion

$$f_{v}=\frac{T\rho}{J}$$

Stress due to Out of Plane Eccentric Load

$$f_{t}=\frac{Mc}{A\sum_{}^{}y^2}$$

$$f_{t}=\frac{Mc}{I}$$

For welds, don’t neglect the first term $I=\frac{bh^3}{12}+Ad^2$

Stress Due to Welds

$$P_{weld}=\sigma_{weld}A_{weld}\to\sigma_{weld}=0.3F_{u}$$

$$A_{weld}=0.707tL$$

Conversion of Electrode Welds

EXX Electrode → Where XX is in Ksi

Convert XX to mPa

1mPa = 145psi

Kips to Newton Conversion

1 kip = 4,448.22 Newtons (N)

Torsional Shearing Stress in Welds

$$f_{vt}=\frac{T\rho}{J}$$

$$J=\sum^{}L\left(\frac{L^2}{12}+x^2+y^2\right)$$

Bending Stress in Beams

$$f_{b}=\frac{Mc}{I}=\frac{M}{S}\to S=\frac{I}{c}$$

Shear Stress in Beams (General)

$$f_{v}=\frac{VQ}{Ib}$$

Average Web Shear Stress (Shear Stress in Web)

$$f_{v}=\frac{V}{d_{tw}}$$

Unit Weight of A36 Steel

$$\gamma=77\frac{kN}{m^3}$$

Allowable Bending Stress

$$F_{b}=0.66Fy$$

Allowable Shear Stress

$F_{V}=0.4F_{y}$ (Allowable Web Shear Stress)

Unless Otherwise Specified

Beam connected to Another Beam → Simply Supported

Beam connected to Column → Fixed

Purlins Design (Max Moment for 1 Sagrod at Midpoint)

$$M_{\max}=\frac{w\left(\frac{l}{2}\right)^2}{8}$$

Interaction Equation for Purlins

$$\frac{f_{bx}}{F_{bx}}+\frac{f_{by}}{F_{by}}\to Ratio$$

Interaction Equation for Purlins (Loads Acting on the Top Flange)

$$\frac{f_{bx}}{F_{bx}}+\frac{2f_{by}}{F_{by}}\to Ratio$$

or $f_{by}=\frac{M_{y}}{\frac{S_{y}}{2}}$