Consider the steel beam with square cross section loaded as shown below.
W= 0.5kN/m
400mm
200mm 200mm
We want to see if a design choice of using a AISI 1050 CD steel beam with a square
cross section of 30 mm is sufficient for strength and what is the factor of safety
Note that for deflections just saying “steel” is usually enough since all varieties of
steel will have more or less same youndgs modulus
But for strength (Sy or Sut) the type of steel and the processing is important. We
will see how this shows up as we do the calculations
Step 1: Use strength of materials to find the location (x,y) in the beam where we
expect failure to occur. This requires actual engineering knowledge not just common
sense. Think back to our first exercise with popsicle sticks. Ring any bells
Step 2: usually we can do this by looking at places where (a) bending moment is
high (b) torque is high (c) shear force is high (d) compression is high (buckling)
In our case we use (a) write singularity functions and draw SFD and BMD (excel
helps here)
Step 2: now find the location of maximum bending moment. It is also the place
where shear force is zero . Why?
Step 3: find the bending moment at the critical location
Step 4: find the stress due to bending moment:
y
P
x
Stress components due to each effect
5: Upto now it is all mechanics, now we come to the materials part. Now look at
material properties:
AISI 1040 CD (Sy 490 MPA) % elongation at failure 12%
Step 6: decision chart:
Step 7: combine stresses, apply the appropriate failure criterion (computing
principal stresses if required)
NOTE: you can only add stress components if they are at the same location
(x,y) AND if they have the same subscripts (PLANE and NORMAL)
You cannot add normal stresses if they act at different points or on
different planes
You cannot add shear stresses if they act at different points, or act on
different planes or if they are in different directions (different subscripts)