Week 7 Challenge- Concepts of Structural Engineering

1) Develop equation for the moment in terms of E ( modulus of elasticity) and moment of inertia (I) and radius of curvature

Ans :-

As,

• M = Bending moment.

• I = Moment of inertia exerted on the bending axis.

• σ = Stress of the fibre at a distance ‘y’ from neutral/centroidal axis.

• E = Youngs modulus of beam material.

• R = Curvature radius of this bent beam.

We know from bending equation

`(M/I)=(E/R)=(sigma/y)`

Where M is moment of inertia and R is radius of curvature.

`M = (E*I)/R`

For a constant bending moment the radius of curvature is constant. It represents a circular bending

2) Define the equations of equilibrium and explain the concept of continuity.

Ans :-

The equilibrium equation describes the static or dynamic equilibrium of all internal and external forces of the system. In the static case, the equilibrium equation is

`K*u = F`

Where,

K is stiffness matrix of the system.

u is vector with nodal displacements.

F represents the external forces.

For system to be in equillibrium, it must satisfy all three equations of equillibrium i.e. sum Fx=0, sum Fy=0 and sum M=0.

3) Give examples for the following

a) Single Force Supports - A person on roller skates.
b) Double Force Support - columns, struts, hangers, braces, pinned truss elements, chains.
c) Rigid Support ( Can explain your examples with diagram) - Rigid support restrain both rotation and translation, this means that a structure only needs one fixed support in order to be stable.

Pole set into concrete is good example of rigid support.

4) What are the common conditions for external instability in a structure?

Ans :- External stabality is when structure does not go rigid body deformations as whole. If reactions are concurrent or parallel external stabality takes place.

5) What are the common conditions for internal instability in a structure?

Ans :- Internal stabality is when each joint in the truss is constraint against rigid body motion. Structure is considered to be internally stable if it maintains its shape and remains rigid when detached from supports.