The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of 8 {kN}. The beam is symmetrical about the neutral axis (N.A.) shown, and the moment of inertia about N.A. is 1.5 \times 10^{9} {mm}^{4}. Considering that the nails at the location {P} are spaced longitudinally (along the length of the beam) at 60 {mm}, each of the nails at {P} will be subjected to the shear force of All dimensions are in mm

GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 49 of 65

Marks: +1, -0

The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of

8 {kN}

. The beam is symmetrical about the neutral axis (N.A.) shown, and the moment of inertia about N.A. is

1.5 × 10^{9} {mm}^{4}

. Considering that the nails at the location

{P}

are spaced longitudinally (along the length of the beam) at

60 {mm}

, each of the nails at

{P}

will be subjected to the shear force of

All dimensions are in mm

Solution:

Shear force in nail at

P=\;{V A \ov{y}}/{l} × \pitch

=\;{8000 × 100 × 50 × 150 {Nmm}^{3}}/{1.5 × 10^{9} {mm}^{4}} × 60 {mm}

=240N

So shear force in nail

=22 × 60=1320 {N}

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