3 3 4 5 Basic Structural analysis B

3. 3. 4, 5 Basic Structural analysis (B. M & S. F, deflection for simply supported and cantilever spans) bkk 1

Shear force and bending moment of beams • Beams: A beam is a structural member resting on supports to carry vertical loads. Beams are generally placed horizontally; the amount and extent of external load which a beam can carry depends upon: a. The distance between supports and the overhanging lengths from supports; b. The type and intensity of load; c. The type of supports; and d. The cross-section and elasticity of the beam. bkk 2

Classification of beams 1. Cantilever Beam 2. Simply supported beam bkk 3

Classification of beams 3. Overhanging Beam 4. Propped Cantilever Beam 5. Fixed Beam bkk 4

SPAN • Clear Span: This is the clear horizontal distance between two supports • Effective Span: This is the horizontal distance between the Centre of end bearings of support. Effective Span = clear span + width of bearing. bkk 5

Bending Moment & Shear Force Diagrams • Bending moment (BM) and shear force (SF) diagrams show the variation of bending moment and shear force along a structural element (beam) when a load (or a set of loads) is applied to the structural element. Points of action of these loads are fixed. • These diagrams are useful to determine the maximum BM and SF developed in the member and the locations of the maximum values due to the application of the loads. 6 bkk 6

Sign Convention - Positive & Negative Values • On the left-hand face of the cut member, positive values; • Normal Force (N) – acts to the right (tends to elongate the segment) • Shear Force (V) – acts downward (tends to rotate the segment clockwise) • Bending Moment (M) - acts counterclockwise (tends to bend the segment concave upward, so as to “hold water”) 3 bkk 7

Positive Normal Force 8 bkk

Positive Shear 9 bkk

Positive Bending Moment 1 0 bkk

BM & SF Diagrams 1 1 bkk

BM & SF Diagrams 1 2 bkk

BM & SF Diagrams 1 3 bkk

BM & SF Diagrams 1 4 bkk

SIMPLY SUPPORTED bkk 15

BM, SF FOR CANTILEVER bkk 16

BM, SF & Reactions 1 7 bkk

DEFLECTION bkk 18

Deflection of Beam • Deflection is the degree to which a structural element is displaced under a load (due to its deformation). It may refer to an angle or a distance. • The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. bkk 19