**Calculation of support reactions of a beam**

**Problem 4-1**

**
Find
the reactions at the support of the following beam shown in figure
4-1(a).**

**Figure 4-1(a)**

**Solution:**

**Figure 4-1(b) ***free-body diagram*

Applying equations of static equilibrium:

ΣF_{x} = 0; **A**_{x}
= 0; (eq. 1)

ΣF_{y} = 0; **A**_{y}
+ **B**_{y} – 10 – 20 × 4 = 0;

**A**_{y}
+ **B**_{y} = 90 kN; (eq. 2)

Considering z-axis passing through A,
and taking moment of all the forces about z-axis *(taking
clockwise –ve and anticlockwise +ve)*;

ΣM_{z} = 0; **B**_{y}
× 10 -10 × 8 – 20 × 4 × 2 = 0 (eq. 3)

Solving eq. 3 yields **B**_{y}
= 24 kN;

Substituting the value of **B**_{y}
in eq. 4-2 gives **A**_{y} = 66 kN.

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