**Slope and deflection calculation by unit load method**

**Problem 7-3**

**Use
unit load method to find the deflection at the center of the
beam shown in figure 7-3(a). Take E= 200 GPa and I=400x10 ^{6}
mm^{4}**

**Figure 7-3(a)**

**Solution:**

In the case of unit load method the deflection at a point of beam is given as

To write the equations of bending moment for different parts of the beam we have to first calculate the support reactions by applying the equations of equilibrium

(i) __reactions due to actual loading__

A_{y} = 13.75 kN; D_{y }=
31.25 kN

write the equations of bending moment for different part of the beam (origin of axes at A).

M_{x} = 13.75x ; (0 ≤ x ≤ 2)

M_{x} = 13.75x - 5(x-2) ;
(2 ≤ x ≤ 4)

M_{x} = 13.75x - 5(x-2) -10(x-4)(x-4)/2; (4 ≤ x ≤
8)

(ii) __reactions due to virtual unit load at C__

a_{y} = 0.5 kN; b_{y}
= 0.5 kN

m_{x} = 0.5x
(0 ≤ x ≤ 4)

m_{x} = 0.5x - 1(x-4)
(4 ≤ x ≤ 8)

Depending upon the validity of different bending moment equations, the deflection at point C can be written as follows;

substituting the appropriate bending moment
equations for M_{x }and m_{x
}

δ_{c}
= 302.58 kN.m^{3}/EI

substituting the values of E I in the above expression we get;

δ_{c}
= (302.58 kN.m^{3})/{(200*10^{6}kN/m^{2})(400*10^{-6}m^{4})}

δ_{c}
= 0.0038 m = 3.8 mm

You can also use our deflection calculator to solve this problem

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