Engineering science

1. Chapter 1- Static engineering systems
1.1 Simply supported beams
1.1.1 determination of shear force
1.1.2 bending moment and stress due to bending
1.1.3 radius of curvature in simply supported beams
subjected to concentrated and uniformly
distributed loads
1.1.4 eccentric loading of columns
1.1.5 stress distribution
1.1.6 middle third rule

2. Types of columns
Depending on the mode of failure, columns can
be categorised in the following ways
(a) a short column
a column which will fail in true compression
(b) a long column
a column which buckles before full compressive strength is
reached

3. Types of beams
• Beams can be classified according to the
manner in which they supported

6. Loads
• Loads can be applied on the beams in one
of the following ways

7. Sheer force and bending moments
• When a beam is loaded
by forces or couples,
internal stresses and
strains are created.
Consider a cantilever
arrangement
• It is convenient to reduce
the resultant to a shear
force, V, and a bending
moment, M.

8. Sign conventions
• Positive shear forces always deform right hand face downward with
respect to the left hand face. Positive shear stress acts clockwise
while negative shear stress acts counter-clockwise
• Positive bending moments always elongate the lower section of the
beam. Positive moment compresses upper (sagging moments)
whereas negative moment compresses lower (hogging moments)

9. Relationships for continuous loads
• Consider the following beam
segment with a uniformly
distributed load with load
intensity q. Note that
distributed loads are positive
when acting downward and
negative when acting upward.
• Summing forces vertically
• Summing moments and
discarding products of
differentials because they are
negligible compared to other
terms

11. Relationships for concentrated loads
• consider the following beam segment
with a concentrated load, P. Again,
concentrated loads are positive when
acting downward and negative when
acting upward.
• Summing forces vertically
• An abrupt change occurs in the shear
force at a point where a concentrated
load acts. As one moves from left to right
through a point of load application, the
shear force decreases by an amount
equal to the magnitude of the downward
load.
• Summing the moments

13. Relationships for couples
• Summing the moments

15. Sheer force and bending moment
diagrams-Concentrated loads

16. Sheer force and bending moment
diagrams-Uniform loads

17. Sheer force and bending moment
diagrams-several concentrated loads

24. Example
• Determine the shear force and bending moment at 1m and
4m from the right hand end of the beam shown in the
figure. Neglect the weight of the beam.
• A cantilever beam that is free at end A and fixed at end B
is subjected to a distributed load of linearly varying
intensity q. The maximum intensity of the load occurs at
the fixed support and is equal to q0. Find the shear force V
and bending moment M at distance x from the free end of
the beam

26. Flexural strains