Solved Problems (Beam deflection)

Solved Problems (Beam Deflections)
Problem 1:

Problem 2:
A 750-hp crane is acquired to lift construction materials in the renovation of CEAT’s poorlydesigned and under-budget buildings. A crane’s boom (beam ABCD) is idealized in the figure
below. However, since the acquired crane is somehow defective, maximum deflection on the
boom should always transpire at the midspan. What should be the weight, W, of the construction
materials to be suspended at point D such that a maximum downward deflection will occur at the
midspan? Also, determine the magnitude of the midspan deflection generated if the boom’s
flexural rigidity is 23.04 kip-in2.
Solution:
Let W = weight of materials
RA = 5 – 0.5W
RC = 15 + 1.5W
Let us consider sectioning at the left most section of the beam:
Moment Equation:

?
W – 15
∴ C2 = -8W + 30 …by substituting C1 on Eq. 2
As the problem stated, the maximum deflection must occur at midspan (midway between
supports). Thus, we can now solve for W by using this condition. Knowing that a maximum
deflection (in between supports) occurs at a tangent line with a zero slope:
At x = 4, θ = 0

EI(0) =

Now, let us solve the maximum deflection occurring at midspan if W = 5 lbs:

Problem 3:
A propped cantilever beam is acted upon by a concentrated load W (lbs) at the free end and a triangular
load with total magnitude of 9W (lbs). Using double integration method, calculate for the maximum
permissible value of W (in lbs) if the maximum downward deflection at C (3 ft. from fixed end) is 0.5 in. and
the slope at the free end is limited to ?
??
degrees. The value of flexural rigidity is 622.08 kip-in2. Also, draw
the elastic curve of beam ABCD. (Hint: Generate two moment equation for each beam.)
Required: WMAX
Solution:
Reactions:

Extend to the right.