By Ian McDonagh (Auth.)
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Extra resources for Mechanical Science for Technicians. Volume 1
20(a) and (b) are plane sections since they are located in the plane, or on the surface, of the paper. First moment of area In the plane section shown in flg. 20(a), the flrst moment TV of the area of the section about the axis XX is N = ΣγδΑ where y is the perpendicular distance of the elemental area bA from the axis XX. Fig. 20 In fig. e. y measured below the axis XX is negative and the total first moment of area about the axis XX is N = N x - N2 or N = Σγ bA For the special case where the axis XX passes through the centroid G of the section, ΣγδΑ or =0 Nt = N2 which it is useful to remember.
88MN/m2] 15 A double-strap butt joint contains a total of twelve rivets, each 5 mm diameter. Calculate the shear stress in each rivet when the joint is subjected to a shearing force of 1 kN. 24 N/mm2 ] 27 16 Define Poisson's ratio. At a point in a material, there is a tensile strain of 8 x 1CT4 and perpendicular to this strain a compressive strain of 3 x 10~4. 3 and the modulus of elasticity is 150GN/m2, calculate the stresses in the direction of the strains. 89 MN/m2 (compressive)] 17 A steel strip, 50 mm x 10 mm x 200 mm long, is subjected to an axial tensile force of 125 kN.
ZZ) which passes through the centroid G will also be zero. I + x4— Y y~ /τ -X d -Y Fig. 21 Second moment of area In the plane section shown in fig. 22, the second moment of area / about the axis XX is 49 Fig. 22 / χ χ - *y2 SA and about axis YY is / Y Y = Σχ2 SA which it is useful to remember. The units for second moment of area are metres to the fourth (m4 ). Second moment of area of common sections For the rectangle shown in fig. 23(a), the second moment of area about the axis XX is given by -bd* 12 / ,_ b ι^ -m Y t• i X- — X i i — -X 1 1 Y (a) Rectangle i Β Y 1 x-4 U | | -Λ L l ï ÜJ 1 a Γ ι 1 (b) Idealised I-section Fig.
Mechanical Science for Technicians. Volume 1 by Ian McDonagh (Auth.)