This document contains multiple engineering problems related to structural analysis, mechanics of materials, steel design, and timber design. For each problem, the question or description is provided along with the corresponding answer. The problems range from easy to difficult in terms of the concepts and calculations required. They cover topics such as stresses, deflections, reactions, strains, flexural strength, temperature effects, torsion, springs, and more. A variety of structural elements, materials, and loading conditions are considered.

1. EASY ROUND
RCD: YOUNG’S MODULUS
ANS: 30 GPa
30s10s5s4s3s2s1sSTOP60s
What is the Young's Modulus of
Elasticity, E, of a High Strength
(compression) Concrete?

2. EASY ROUND
STATICS: SUPPORT REACTION
ANS: FAx= 21.65 Kn ; FAy= 92.5 kN ; MA= 457.5 kN·m
30s10s5s4s3s2s1sSTOP60s
Determine the support reactions at A.

3. EASY ROUND
STRUCTURAL THEORY:
SLOPE AND DEFLECTION
ANS: iA= 0.0023 rad ; yC= 2.3 mm
30s10s5s4s3s2s1sSTOP60s
A simply supported beam of span 3-m is
subjected to a central load of 10 kN. Find the
maximum slope and deflection of the beam.
Take I= 12 x 106 mm4 and E= 200 GPa.

4. EASY ROUND
STRUCTURAL THEORY:
SHEAR AND MOMENT DIAGRAMS
ANS:
30s10s5s4s3s2s1sSTOP60s
Construct the shear and moment diagram of
the beam loaded as shown.

5. AVERAGE ROUND
STRENGTH OF MATERIALS: ELONGATION
ANS: 38.605 x 10-4 m
30s10s5s4s3s2s1sSTOP60s3 mins2 mins
A steel wire of length 1.3 m and diameter 0.90 mm is
joined to an aluminum wire of identical dimensions
to make a composite wire of length 2.6 m. Find the
resulting change in length of this composite wire if
an object with a mass of 5.00 kg is hung vertically
from one of its ends. (Neglect any effect the masses
of two wires have on the changes in their lengths.)
Est= 200 x 109 N/m2 ; Eal= 70 x 109 N/m2

6. AVERAGE ROUND
TIMBER DESIGN: STRESSES
ANS: 5100 kPa
30s10s5s4s3s2s1sSTOP60s3 mins2 mins
A 100-mm-by-100mm (S4S) timber beam on a
simple span of 4 m is subjected to vertical and
lateral point loads placed at midspan. The lines
of action of the loads pass through the centroid
of the cross section. Determine the stresses at
the CORNERS of the cross section at the point
of maximum moment?

7. AVERAGE ROUND
DYNAMICS: VELOCITY
ANS: vA= 3.11 m/s ; vB= 1.798 m/s
30s10s5s4s3s2s1sSTOP60s3 mins2 mins
The motion of the slender 10
kg rod AB is guided by collars
of negligible mass that slide
freely on the vertical and
horizontal rods shown.
Knowing that the bar is
released from rest when θ = 30 degrees, determine
the velocity of collars A and B when θ = 60 degrees.

8. AVERAGE ROUND
STEEL DESIGN: TEMPERATURE
ANS: 47.08 °C
30s10s5s4s3s2s1sSTOP60s3 mins2 mins
As the drawing shows, two thin strips of metal are
bolted together at one end and have the same
temperature. One is steel, the other is lead. The steel
strip is 0.08% longer than the lead strip. By how
much should the temperature(C°) of the strips be
increased, so that the strips have the same length?

9. DIFFICULT ROUND
MECHANICS OF MATERIALS: STRAIN
ANS: ϵBC= 0.00446 mm/mm ; γAxy= -0.00741 rad
30s10s5s4s3s2s1sSTOP60s5 mins4 mins3 mins2 mins
The triangular plate is
deformed into the shape
shown by the dashed line.
Determine the normal
strain developed along edge
BC and the average shear
strain at corner A with
respect to the x and y axes.

10. DIFFICULT ROUND
RCD: FLEXURAL STRENGTH
A tensile-reinforced beam has b = 12 in. and d =
20 in. to the center of the bars, which are
placed all in one row. If fy = 60,000 psi and fc’ =
5000 psi, find the nominal flexural strength Mn
for (a) As = two No. 8 bars, and (b) As = two No.
10 bars.
ANS: (a) Mn= 1.8 x 106 in·lb ; (b) Mn= 2.82 x 106 in·lb
30s10s5s4s3s2s1sSTOP60s5 mins4 mins3 mins2 mins

11. DIFFICULT ROUND
STRENGTH OF MATERIALS:
HELICAL SPRING
A closely-coiled helical spring of round steel
wire 5 mm in diameter having 12 complete
coils of 50 mm mean diameter is subjected to
an axial load of 100 N. Find the deflection of
the spring and the maximum shearing stress in
the material. Modulus of rigidity = 80 GPa.
ANS: δ= 24 mm ; τ= 101.9 MPa
30s10s5s4s3s2s1sSTOP60s5 mins4 mins3 mins2 mins

12. DIFFICULT ROUND
MECHANICS OF MATERIALS: TORSION
ANS: τo= 0.345 MPa ; τi= 0.276 MPa
30s10s5s4s3s2s1sSTOP60s5 mins4 mins3 mins2 mins
The pipe shown has an inner
diameter of 80 mm & an outer
diameter of 100 mm. If its end
is tightened against the support
at A using a torque wrench at B,
det. the shear stress developed
in the material at the inner and
outer walls along the central portion of the pipe when
80-N forces are applied to the wrench.