Mechanics Of Rigid Bodies

Mechanics of rigid bodies

Analysis of Truss This truss structure represents part of a bridge. Calculate the force in each strut when the bridge is supporting a 7200N load at its center

A bridge of length 50.0 m and mass 8.00 X 104 kg is supported in a smooth pier at each end as in Figure. A truck of mass 3.00X 104 kg is located 15.0 m from one end. What are the forces on the bridge at the points of support?

Ex1:

A 200-kg load is hung on a wire having a length of 4.00 m cross-sectional area 0.200 X10-4m2, and Young’s modulus 8.00X 1010N/m2. What is its increase in length? EX2 : Assume that Young’s modulus is 1.50 X 1010 N/m2 for bone and that the bone will fracture if stress greater than 1.50X 108 N/m2 is imposed on it. (a) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.50 cm? (b) If this much force is applied compressively, by how much does the 25.0cm-long bone shorten?

Internal forces Forces in beams

Shear force & bending moments At a section of a beam;

M

Y

R X

Z Y

My Sy

R P

X

SZ

Z

Mx

MZ

Beams are classified according to their support conditions • Simply supported beam

• Cantilevered beam

• Propped cantilever

• Overhanging beam

Shear force & bending moments W

Bending moments – sign convention • Hogging moments – Positive

• Sagging moments Negative

Shear forces – sign convention • Clockwise shear – Positive

• Anticlockwise shear Negative

EX1: A cantilever beam with the concentrated load W at the free end. Draw bending moment diagram and shear force diagram.

W

EX2: A simply supported beam AB with the concentrated load W at a distance of a from support A. Draw bending moment diagram and shear force diagram.