A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensionsof b1 = 14 in., d1 = 2.2 in., b2 = 2.2 in., d2 = 13 in., b3 = 7 in., and d3 = 2.2 in.%3D(a) Determine the distance from the bottom edge of the section to the centroid.(b) Determine the moment of inertia of the section about the z axis.(c) Determine the maximum shear stress in the cross section if the internal shear force is V = 480 lb.Assume that the shear force Vacts in the y direction.(d) Consider nail B that connects the bottom flange to the beam web. If the nails used at B can provide150 Ib of horizontal resistance (in the x direction), determine the maximum nail spacing s (in the xdirection) that can be used for nail B. Assume V = 480 lb.(e) If a bending moment applied about the z axis produces a tension normal stress of ox = 510 psi atthe bottom of the cross section, determine the compression normal stress produced at the top of thecross section.b1y|Nail Adid2b2dzNail Bb3

Area A1=b1×d1=14×2.2=30.8 in2C.G of area A1 from top y1=d12=1.1 in⇒Area A2=b2×d2=2.2×13=28.6…

A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensions of b1 = 14 in., d1 = 2.2 in., b2 = 2.2 in., d2 = 13 in., b3 = 7 in., and d3 = 2.2 in. (a) Determine the distance from the bottom edge of the section to the centroid. (b) Determine the moment of inertia of the section about the z axis. (c) Determine the maximum shear stress in the cross section if the internal shear force is V = 480 lb. Assume that the shear force Vacts in the y direction.

A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensions of b1 = 14 in., d1 = 2.2 in., b2 = 2.2 in., d2 = 13 in., b3 = 7 in., and d3 = 2.2 in. (a) Determine the distance from the bottom edge of the section to the centroid. (b) Determine the moment of inertia of the section about the z axis. (c) Determine the maximum shear stress in the cross section if the internal shear force is V = 480 lb. Assume that the shear force Vacts in the y direction.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Moments

There are various practical applications of the concept of moments, like a rotation of the crank due to linear motion of the piston, the moment of inertia and its use in designing beams and columns, bending moment concept, torque, twisting moment, etc.

Question

A wooden beam is fabricated by nailing together three boards as shown. The boards have dimensions
of b1 = 14 in., d1 = 2.2 in., b2 = 2.2 in., d2 = 13 in., b3 = 7 in., and d3 = 2.2 in.
%3D
(a) Determine the distance from the bottom edge of the section to the centroid.
(b) Determine the moment of inertia of the section about the z axis.
(c) Determine the maximum shear stress in the cross section if the internal shear force is V = 480 lb.
Assume that the shear force Vacts in the y direction.
(d) Consider nail B that connects the bottom flange to the beam web. If the nails used at B can provide
150 Ib of horizontal resistance (in the x direction), determine the maximum nail spacing s (in the x
direction) that can be used for nail B. Assume V = 480 lb.
(e) If a bending moment applied about the z axis produces a tension normal stress of ox = 510 psi at
the bottom of the cross section, determine the compression normal stress produced at the top of the
cross section.
b1
y|
Nail A
di
d2
b2
dz
Nail B
b3

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