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How is the load distributed to the members in the angular axis method if the members are excluded from the load application?

Answer

A surface load of 1 kN/m² delimited by nodes 1 to 4 is only applied to member 3 (Figure 1).

Image 01 - Area Load

The entries made in the load generator are shown in Figure 02. There is no correction of the distribution according to the moment equilibrium (Figure 3).

Image 02 - Settings for Converting Area Loads to Member Loads

Image 03 - Settings for Load Generation via Plane

The generated member load is shown in Figure 4. This is calculated as follows:

q = 1.00 kN/m² (area load)

h1 = 4.00 m

h2 = 6.00 m

btot = 12.00 m

$\mathrm\alpha\;=\;\arctan\left(\frac{{\mathrm h}_2\;-\;{\mathrm h}_1}{{\mathrm b}_{\mathrm{ges}}}\right)\;=\;\arctan\left(\frac{6,000\;-\;4,000}{12,000}\right)\;=\;9,46^\circ$

${\mathrm b}_1\;=\;\tan\left(\mathrm\alpha\right)\;\cdot\;{\mathrm h}_1\;=\;\tan\left(9,46^\circ\right)\;\cdot\;4,000\;=\;0,667\;\mathrm m$

${\mathrm l}_1\;=\;\sqrt{{\mathrm b}_1^2\;+\;{\mathrm h}_1^2}\;=\;\sqrt{0,667^2\;+\;4,000^2}\;=\;4,055\;\mathrm m$

${\mathrm l}_2\;=\;\cos\left(\mathrm\alpha\right)\;\cdot\;{\mathrm h}_2\;=\;\cos\left(9,46^\circ\right)\;\cdot\;6,000\;=\;5,918\;\mathrm m$

$ {\mathrm A} _ {\mathrm R}\; =\frac {\; {\mathrm b} _1\;\cdot\; {\mathrm h} _1} 2\; =\;\frac {\; 0.667\;\cdot\; 4,000} 2\; =\; 1.335\;\mathrm m ^ 2 $ (remaining area marked in red in Figure 4)

${\mathrm l}_{\mathrm{ges}}\;=\;\sqrt{{\mathrm b}_{\mathrm{ges}}^2\;+\;\left({\mathrm h}_2\;-\;{\mathrm h}_1\right)^2}\;=\;\sqrt{12,000^2\;+\;\left(6,000\;-\;4,000\right)^2}\;=\;12,166\;\mathrm m$

$ {\mathrm q} _ {\mathrm c}\; =\:\frac {\mathrm q\;\cdot\; {\mathrm A} _ {\mathrm R}} {{\mathrm l} _ {\mathrm {ges}}}\; =\;\frac {1.00\;\cdot\; 1.333} {12.166}\; =\; 0.110\;\mathrm {kN}/\mathrm m $ (constant load component on loaded member)

$ {\mathrm q} _2\; =\: {\mathrm q} _ {\mathrm c}\; +\; {\mathrm l} _1\;\cdot\;\mathrm q\; =\;\: 0.110\; +\; 4.055\;\cdot\; 1,000\; =\; 4.165\;\mathrm {kN}/\mathrm m $ (member load node 2)

$ {\mathrm q} _5\; =\: {\mathrm q} _ {\mathrm c}\; +\; {\mathrm l} _2\;\cdot\;\mathrm q\; =\;\: 0.110\; +\; 5.918\;\cdot\; 1,000\; =\; 6.028\;\mathrm {kN}/\mathrm m $ (member load node 5)

q4 = qc = 0.110 kN/m (member load node 4)

Image 04 - Generated member load from area load

Keywords

Load generator Generated load Load Distribution Type Angular axes

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  • Updated 12/01/2020

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