CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader همد 202- نظرية الإنشاءات (2) (3 ساعات معتمدة) المتطلب السابق همد 201 خواص المساحات المستوية – الإجهادات المحورية – اجهادات القص )قوي القص – عزم الالتواء( – الإجهادات المركبة والأساسية . CIV 202 - Theory of Structures (2) (3 Credit Hours) Prerequisite CIV 201 Properties of plane areas – normal stresses – shear stresses (shearing force – torsional moment) – combined and principle stresses.

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Properties of Areas Centroid Moments of inertia Radius of gyration Principal axes of inertia Centroids of general bodies Stresses Normal Stresses (due to normal force and bending moment) Shear Stresses (due to shear force and twisting moment) Principal Stresses

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Centroid - Area: It is always a positive quantity and its dimension is a length square (mm2, cm2, m2, ...). - First moment of area about the y-axis: It is the product of the area A and the distance .

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Centroid For simple symmetrical shapes (e.g.; rectangle, circle, …), the position of the centroid is obvious. For shapes having an axis of symmetry, the centroid lies on this axis of symmetry For shapes having more than axis of symmetry, the centroid lies on the intersection point of these axes of symmetry For shapes symmetric about a point, like the Z-section, the center of symmetry is the centroid.

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Centroid Example: Calculate the first moment of area for the shown shape about the x-axis (bottom edge). Also, find the position of the centroid. Solution: The centroid is 32.273 mm from the bottom edge.

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Centroid Example: Determine the position of the centroid of the shown area. Solution: The centroid is 8.51 cm from the left edge and 4.61 cm from the bottom edge.

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Centroid Example: Determine the position of the centroid of the shown area. Solution: The centroid is 0.651 m from the bottom edge.

CIV 202 - THEORY OF STRUCTURES (2) Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader Centroid Example: Determine the position of the centroid of the shown steel cross-section. The properties of the channel and the angle are as given: Solution: The centroid is 8.62 cm from the left edge and 12.45 cm from the bottom edge.

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