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Centroids of simple shapes
Published in John Bird, Bird's Engineering Mathematics, 2021
The first moment of area is defined as the product of the area and the perpendicular distance of its centroid from a given axis in the plane of the area. In Fig. 54.1, the first moment of area A about axis XX is given by (Ay) cubic units.
Fluid mechanics
Published in William Bolton, Engineering Science, 2020
The product of an area element and its distance from some axis is called the first moment of area. Thus, as the first moment of area about O is AY, then: yc=second moment of area about Ofirst moment of area about O
First and second moments of area
Published in John Bird, Carl Ross, Mechanical Engineering Principles, 2019
The first moment of area is defined as the product of the area and the perpendicular distance of its centroid from a given axis in the plane of the area. In Figure 9.1, the first moment of area A about axis XX is given by (Ay) cubic units.
Experimental analysis of the shear behaviour of prestressed and reinforced concrete beams
Published in European Journal of Environmental and Civil Engineering, 2018
Kristof De Wilder, Guido De Roeck, Lucie Vandewalle
In Equations (6) and (7), Asl represents the total area of tensile longitudinal reinforcement, I is the second moment of area whereas S denotes the first moment of area. Finally, fctd represents the design value of the uni-axial tensile strength, whereas αl is a factor taking into account the bond properties of the longitudinal reinforcement. If the above-outlined equations are used to estimate the actual shear capacity of a structural concrete member, all partial safety factors should be omitted and average material strengths should replace the characteristic values. Hence, Equations (2)–(3) and (5)–(7) are transformed and given in Equations (8)–(12).