Find the support reactions and the slope of the elastic beam at A. The beam has a rectangular cross section (100mm times 300mm) and the modulus of elasticity is 20 GPa. Solution As we know that there is a gap at the section by 2mm So there will be reactions at A and B Ra + Rb = 5Kn Assume moment at A = 0 Rb x 6 - 5x2 = 0 Rb = 1.67Kn hence Ra = 5-Rb = 5-1.67 = 3.33kn as we know the slope equation for this type of point with varying distances is Slope at A i = (Wb/6EIL) (L 2 - a 2 ) W = 5kn b = 4m = 4000mm a = 2m = 2000mm L = 6m = 6000mm I = moment of inertia moment of inertia for a rectangular section (100 x 300)mm I = (bd 3 /12) b= 100mm D = 300mm I = (100 x 300 3 /12) = 225 x 10 6 mm4 E = 20Gpa = 20 x 1000 Mpa Slope at A i = (Wb/6EIL) (L 2 - a 2 ) i = (5x1000 x 4000/6x20 x 1000 x 225 x 10 6 x 6000) (6000 2 - 2000 2 ) i = 0.003952 rad .

1. Find the support reactions and the slope of the elastic beam at A. The beam has a rectangular
cross section (100mm times 300mm) and the modulus of elasticity is 20 GPa.
Solution
As we know that there is a gap at the section by 2mm
So there will be reactions at A and B
Ra + Rb = 5Kn
Assume moment at A = 0
Rb x 6 - 5x2 = 0
Rb = 1.67Kn
hence Ra = 5-Rb = 5-1.67 = 3.33kn
as we know the slope equation for this type of point with varying distances is
Slope at A
i = (Wb/6EIL) (L 2
- a 2
)
W = 5kn
b = 4m = 4000mm
a = 2m = 2000mm
L = 6m = 6000mm
I = moment of inertia
moment of inertia for a rectangular section (100 x 300)mm

2. I = (bd 3
/12)
b= 100mm
D = 300mm
I = (100 x 300 3
/12) = 225 x 10 6
mm4
E = 20Gpa = 20 x 1000 Mpa
Slope at A
i = (Wb/6EIL) (L 2
- a 2
)
i = (5x1000 x 4000/6x20 x 1000 x 225 x 10 6
x 6000) (6000 2
- 2000 2
)
i = 0.003952 rad