   Chapter 8, Problem 8.2.4P

Chapter
Section
Textbook Problem

The fasteners in the connection of Figure P8.2-4 are placed at the workable gage distance shown in Manual Table 1-7A. What additional force is experienced as a consequence of the fasteners not being on the centroidal axis of the member? To determine

The additional force experienced as a consequence of the fastener not being on the centroidal axis of the member.

Explanation

Concept used:

Write the expression for total shear force in the fastener.

p=(px2)+(py2)

Here, the total load coming on critical bolt due to eccentricity in x direction is px, the total load coming on critical bolt due to eccentricity in y direction is py, and the total shear force in fastener is p.

Calculation:

Write the expression for the load which is coming on each of the bolt in x-direction.

Pex=Pxn     ...... (I)

Here, the load component in x direction is Px, load which is coming on each of the bolt in x-direction is Pex, and the number of bolt is n

Substitute 70k for Px and 5 for n in Equation (I).

Pex=70k5=14k

Write the expression for the load on each of the bolt in the y-direction.

Pey=Pyn     ...... (II)

Here, the load component in the y direction is Py, load which is coming on each of the bolt in y-direction is Pey and the number of bolt is n.

There is no load acting in the y direction, so Pey is zero.

Write the expression to calculate the location of the centroid with respect to the lower left bolt.

x¯=(n×d)T ..... (III)

Here, the number of bolts is n, the distance of the bolts is d, and the total number of bolts is T.

Substitute the values in Equation (III).

x¯=(9×1)+(6.75×1)+(4.5×1)+[2.25×1]5=4.5in

Write the expression to calculate the location of the centroid with respect to the lower left bolt.

y¯=(n×d)T ..... (IV)

Here, the centroid of y¯ is zero.

Calculate the eccentricity of the load that is the distance from the middle of the bracket connection to the point of load in both x and y directions from the Figure-1 diagram given below.

Figure-(1)

Calculate the distance of the load from the middle of the connection.

ex=4.5in

ey=1.58in

Here, the eccentricity in x direction is ex and the eccentricity in y direction is ey.

Write the expression to calculate horizontal and vertical components of the loads caused due to eccentricity.

Σ(x2+y2)=(2.25in)2×2+(4.5in)2×2=50.63in2

Write the expression for the moment for x-axis about midpoint of the connection between the bolts.

Mx=Px×ey ..... (V)

Here, moment generated is x direction is Mx.

Substitute 70k for Px and 1.58in for ey in Equation (V).

Mx=70k×1.58in=110.6in-k

Write the expression for the moment for y-axis about midpoint of the connection between the bolts.

My=Py×ex ..... (VI)

Here, moment generated is y direction is My.

There is no load acting y direction, so Pey is zero

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