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Calculate the shear force and bending moment values due to the imposed loading on the overhanging beam of Figure 1.

The free-body-diagram is shown in Figure 2. The beam’s reactions are calculated as:

ΣF_{x}^{ }= 0 -> **A _{x} = 0**

ΣΜ_{Α} = 0 -> Β_{Y}x6 - 30x10 -5x4x4 = 0-> **Β**_{Y }**=63.33kN **

ΣF_{Y }= 0 -> A_{Υ} + B_{Υ} = 5x4 + 30 -> **A _{y} =-13.33kN**

**Calculations of shear force**

Shear force is calculated in both sides (left and right) of each point.

F_{A-right} = -13.33kN

F_{C} = -13.33kN

F_{B-left} = -13.33 – 5x4 = - 33.33kN

F_{B-right} = -13.33 – 5x4 + 63.33 = +30kN

F_{D-left} = +30kN

**Calculations of bending moment **

Bending moment is calculated as follow (same left and right):

M = 0

M = –13.33x2 = -26.66kNm

M = –13.33x6 – 5x4x2 = –80 –40 = –120kNm

M = 0

**Shear force and bending moment plots**

The following Figure 3 presents the plots of shear force and bending moment.

Some interesting points should be outlined:

1. The maximum bending moment will occur at the point where shear force changes sign. Point B is such a point.

2. The bending moment sign does not change, hence there is no point of contra-flexure. The bending moment diagram is a straight line from point A to C, a parabolic curve from C to B and a straight line from B to D.

Structural AnalysisTruss deflection using the unit load methodMethod of sectionsBending stress in a beam elementCalculation of the cross-sectional area and the position of centroidCalculation of the second moments of area

Buckling

1 pages

Confinement (structural)

Elasticity and Inelasticity

Fatigue

Moment distribution

Nonlinear analysis

Structural stability

1 pages

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