The internal shear force at a certain section of a steel beam is V= 8.8 kN. The beam cross-section shown in the figure has dimensions of b= 141 mm, c= 31 mm, d= 63 mm, and t= 6 mm. Determine: (a) the shear stress at point H. (b) the shear stress at point K. (c) the maximum horizontal shear stress in the cross section. Break the cross section into five rectangles, as shown. It is seen that the two labeled with a (1) are identical, and the two labeled with a (2) are identical. Find A1, the area of rectangles (1), and y1, the vertical distance from the bottom edge of the cross-section to the centroid of rectangles (1). Similarly, find A2, the area of rectangles (2), and y2, the vertical distance from the bottom edge of the cross-section to the centroid of rectangles (2). Then, find A3 and y3 for rectangle (3). A1= mm2 y1= mm A2= mm2 y2= mm A3= mm2 y3= mm Find Iz, the area moment of inertia about the z centroidal axis for the cross-section. Iz= mm4 Part 4 Find QH, the first moment of area about the z centroidal axis for the entire area below point H. This area has width 2c and height t. Also, find QK, the first moment of area about the z centroidal axis for the entire area above point K with width b and height t. QH= mm3 QK= mm3 Part 5 Determine the magnitudes of the shear stress at point H and the shear stress at point K. τH= MPa τK= MPa Part 6 Find Qmax, the maximum first moment of area about the z centroidal axis for any point in the cross section, and τmax, the maximum horizontal shear stress magnitude in the cross section. Qmax= mm3 τmax= MPa
The internal shear force at a certain section of a steel beam is V= 8.8 kN. The beam cross-section shown in the figure has dimensions of b= 141 mm, c= 31 mm, d= 63 mm, and t= 6 mm. Determine:
(a) the shear stress at point H.
(b) the shear stress at point K.
(c) the maximum horizontal shear stress in the cross section.
Break the cross section into five rectangles, as shown. It is seen that the two labeled with a (1) are identical, and the two labeled with a (2) are identical. Find A1, the area of rectangles (1), and y1, the vertical distance from the bottom edge of the cross-section to the centroid of rectangles (1). Similarly, find A2, the area of rectangles (2), and y2, the vertical distance from the bottom edge of the cross-section to the centroid of rectangles (2). Then, find A3 and y3 for rectangle (3).
| A1= | mm2 |
| y1= | mm |
| A2= | mm2 |
| y2= | mm |
| A3= | mm2 |
| y3= | mm |
Find Iz, the area moment of inertia about the z centroidal axis for the cross-section.
Iz= mm4
Part 4
Find QH, the first moment of area about the z centroidal axis for the entire area below point H. This area has width 2c and height t. Also, find QK, the first moment of area about the z centroidal axis for the entire area above point K with width b and height t.
| QH= | mm3 |
| QK= | mm3 |
Part 5
Determine the magnitudes of the shear stress at point H and the shear stress at point K.
| τH= | MPa |
| τK= | MPa |
Part 6
Find Qmax, the maximum first moment of area about the z centroidal axis for any point in the cross section, and τmax, the maximum horizontal shear stress magnitude in the cross section.
| Qmax= | mm3 |
| τmax= | MPa |
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