Analysis Results

Here are the possible beams that support the inputs

List of beams that passed

<table>

{% for key in outputs.dimensions %}

{% endfor %}

</table>

Beams

{% for key in outputs.dimensions %}

_______________________________________________________________________________________

<a href="#{{key}}" id="{{key}}">{{key}}</a>

{% set load_var = "M_r = \\frac{w_fL^2}{8} = \\frac{" + outputs.load +"\\times" + outputs.L + "^2}{8}" %}

The distributed factored load is {{ load_var | katex }}

{% set m_var = "M_{ry} = " + outputs.Mr + "\\frac{KN}{m}" %}

{{ m_var | katex }}

Assume section is class 2. (This assumption must be verified after selection of a section)

{% set zy_1 = "Z_y = \\frac{M_{ry}}{\\phi F_y} = \\frac{" + outputs.Mr + "} {0.9 \\times" + outputs.Fy + "}" %}

{{ zy_1 | katex }}

{% set zy_2 = "Z_y = " + outputs.Zy + "mm^3" %}

{{ zy_2 | katex }}

pick a W section where the beam's $Z_y$ is greater than the calculated $Z_y$

Here are the following properties for this beam:

<table>

<tr><th>Property</th><th>Value</th>

<tr><td> $d$ </td><td>{{outputs.keys[key]['d'] | katex}} $mm$ </td></tr>

<tr><td> $b$ </td><td>{{outputs.keys[key]['b'] | katex}} $mm$ </td></tr>

<tr><td> $t$ </td><td> {{outputs.keys[key]['t'] | katex}} $mm$ </td></tr>

<tr><td> $w$ </td><td>{{outputs.keys[key]['w'] | katex}} $mm$ </td></tr>

<tr><td> $I_y$ </td><td>{{outputs.keys[key]['Iy'] | katex}} $\times 10^6 \ mm^4$ </td></tr>

<tr><td> $S_y$ </td><td>{{outputs.keys[key]['Sy'] | katex}} $\times 10^3 \ mm^3$ </td></tr>

<tr><td> $Z_y$ </td><td>{{outputs.keys[key]['Zy'] | katex}} $\times 10^3$ $mm^3$ </td></tr>

</table>

Test for class 1/2:

For the flange:

{% set flange_var = "\\frac{b_{el}}{t} = \\frac{" + outputs.keys[key]['b'] + "}{2\\times" + outputs.keys[key]['t'] + "} = " + outputs.out1[key]['flange'] + "\\leq \\frac{170}{\\sqrt{F_y}} = " + outputs.flangetest %}

{{ flange_var | katex }}

For the web:

{% set web_var = "\\frac{h}{t} = \\frac{" + outputs.keys[key]['d'] + " - " + outputs.keys[key]['t'] +"\\times 2 }{" + outputs.keys[key]['w'] + "} = " + outputs.out1[key]['web'] + "\\leq \\frac{1700}{\\sqrt{F_y}} = " + outputs.webtest %}

{{ web_var | katex }}

The factored Moment resistance:

{% set moment_var = "M_{ry} = \\phi Z_y F_y = 0.9 \\times" + outputs.keys[key]['Zy'] + "\\times" + outputs.Fy + " = " + outputs.out1[key]['Mr'] + "kNm > M_{ry} = " + outputs.Mr + "kNm" %}

{{ moment_var | katex }}

Check the shear capacity of the section for shear:

In this case shear must be carried by two flanges. Using the mechanics of material equation, the shear stress

distribution is $\tau = \frac{V_xQ_y}{I_yt}$ , in which $Q_y$ is the statical moment of area at the section of

interest is, and $V_x$ is the applied shear force. Shear stress distribution is parabolic with the maximum at the

mid-point of the flange. At that location,

{% set var_1 = "Q_y = \\bigl( \\frac{1}{2}bt\\bigr)\\bigl(\\frac{1}{4}b\\bigr) = \\frac{1}{8}b^2t" %}

{{ var_1 | katex }}

{% set var_2 = "Q_y = " + outputs.out[key]['Qy'] + "\\times 10^3 mm^3" %}

{{ var_2 | katex }}

{% set var_3 = "V_x = \\frac{1}{2}V_f = \\frac{1}{2}\\frac{w_fL}{2}" %}

{{ var_3 | katex }}

{% set var_4 = "V_x = " + outputs.out[key]['Vx'] + "kN" %}

{{ var_4 | katex }}

{% set var_5 = "\\tau = " + outputs.out[key]['tao'] + "MPa < 0.60F_y = " + outputs.t + "Mpa" %}

{{ var_5 | katex }}

{% endfor %}

CSA S16-2

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