An aluminum extrusion has the shape shown in the figure where b= 38 mm, d= 52 mm, a= 10 mm, and t= 2 mm. A vertical shear force of V= 2500 N acts on the cross section. Determine the shear flow that acts in the shape at points A–D. Part 1 Break the cross section into five rectangular areas, as shown. Find the area A1 of area (1) and the vertical distance y1 from the bottom edge of the cross-section to the centroid of area (1). Similarly, find the areas of the other four rectangles, and the vertical distance from the bottom edge of the cross section to the centroid of each. A1= 104 mm2 A2=A3= 20 mm2 A4=A5= 32 mm2 y1= 26 mm y2=y3= 5 mm y4=y5= 1 mm Part 2 Find y¯, the vertical distance from the bottom edge of the cross section to the centroid of the cross section. y¯= 14.27 mm
An aluminum extrusion has the shape shown in the figure where b= 38 mm, d= 52 mm, a= 10 mm, and t= 2 mm. A vertical shear force of V= 2500 N acts on the cross section. Determine the shear flow that acts in the shape at points A–D.
Part 1
Break the cross section into five rectangular areas, as shown. Find the area A1 of area (1) and the vertical distance y1 from the bottom edge of the cross-section to the centroid of area (1). Similarly, find the areas of the other four rectangles, and the vertical distance from the bottom edge of the cross section to the centroid of each.
| A1= | 104 mm2 |
| A2=A3= | 20 mm2 |
| A4=A5= | 32 mm2 |
| y1= | 26 mm |
| y2=y3= | 5 mm |
| y4=y5= | 1 mm |
Part 2
Find y¯, the vertical distance from the bottom edge of the cross section to the centroid of the cross section.
y¯= 14.27 mmPart 3
Find Iz, the area moment of inertia about the z centroidal axis for the cross-section.
Iz= mm4Part 4
Consider point A, and find the first moment of area about the z centroidal axis, QA, and the shear flow that acts at A, qA.
| QA= | mm3 |
| qA= | N/mm |
Part 5
Consider point B, and find the first moment of area, QB, and the shear flow, qB.
| QB= | mm3 |
| qB= | N/mm |
Part 6
Consider point C, and find the first moment of area, QC, and the shear flow, qC.
| Qc= | mm3 |
| qc= | N/mm |
Part 7
Consider point D, and find the first moment of area, QD, and the shear flow, qD.
| QD= | mm3 |
| qD= | N/mm |
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