Draw the shear and bending moment diagram of the following beams using area method. Also make a summary table for the following values:

a. End reactions and moments (R _left , M _left ,R _right , M _right )

b. Maximum positive and negative bending moment and locations (measured from left end)

3) Type of span: Simply supported

Span length: 20 ft.

Beam Loadings:

• Uniformly distributed load of 20 kips/ft., acting along the entire length of the beam

• Point load (downward) 25 kips, at the left support

• Point load (downward) 50 kips, 5ft from left support

• Point load (downward) 75 kips, 10 ft. from left support

• Point load (downward) 100 kips, 15 ft. from left support

4) Type of span: Cantilever (fixed at right end)

Span length: 8m

Beam Loadings:

• Uniformly distributed load 10 k N/m along the entire span

• point load (downward) 20 kN, 4 m from the free end

• Point load (upward) 20 kN , 2 m from the fixed end

• Clockwise moment 40 kN-m at the free end

5) Type of span: Overhanging (supports are located 8 ft. from the ends)

Span length: 24 ft.

Beam loadings:

• Varying load from 0 to 60 kips/ft. acting from left end to the left support

• Uniformly distributed load 45 kips/ft. acting from left support to the right support

• Varying load from 60 kips/ft. to 0, acting from the right support to the right end