determine the shear axial force and bending moment Determine

determine the shear axial force and bending moment

Determine the internal shear, axial force, and bending moment in the bean at points C and D. Assume the support at theta is a roller. Point C is located just to the right of the 8-k load.

Solution

The rection forces acting on the beam under equilibrium,

Ra + Rb = 8 --- eqn 1

Ha = 0

Taking moment about A,

Ma = 0

Rb x 24 - 8 x 8 = 0

Rb = 2.66 klb

So, Ra = 8 - Rb = 8 - 2.66 = 5.33 klb

Determine moment about D,

Md = 40 + Rb x 8 = 40 + 2.66 x 8 = 61.28 klb-ft

Now determine the moment at C,

Mc = 0

Ra x (8+y) - 8y -40 - Rb (16-y) = 0

5.33 x 8 - 5.33y - 8y - 40 - 2.66 x 16 + 2.66y = 0

10.67y = 42.64 - 40 - 42.56

y = 3.74 ft

Now Mc = Ra x (8+3.74) - 8x 3.74 = 62.57 - 29.9 = 32.67 klb-ft

SF at C:

Ra - 8 = 5.33 - 8

SF_c = (-) 2.67 klb

SF at D:

SF_c + Rb = -2.67 + 2.66 = (-) 0.01 lbf

SF_d = (-) 0.01 klbf