homework 1 problem 1 25 in your own words answer the following questio

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HOMEWORK 1
Problem 1 (25%)
In your own words, answer the following questions
(a) Name three concrete admixtures used in concrete. Explain the purpose of each admixture.
(b) Draw a graph of the water-to-cement (W/C) ratio versus concrete strength. Does the addition of
water in a concrete mix reduce its strength? Explain.
(c) Explain the concept of creep and shrinkage. Give an example of a typical situation where each
phenomenon would be most noticeable.
(d) Why is it important to maintain the concrete moist through curing at its early age?
1 Homework 1
Problem 2 (25%)
The beam below carries its own weight and two concentrated loads. The unit weight of concrete is 150 pcf
and the modulus of rupture is 410 psi. Do the following:
(a) Draw the bending moment diagram and show the bending moment values in terms of P1.
(b) The concentrated loads are equally increased until cracking occurs at the bottom face of the beam. What
is the value of the concentratred load P₁ that causes cracking?
(c) Assuming the P1
=
0 kip and a concentrated load P2 is applied at each cantilever tip (points A and D in
the figure). What is the value of P2 that causes cracking of the beam at the supports (points B and C in the
figure)?
C.A
Al
ΔΒ
P₁
1
P₁
1
12 ft
10 ft
10 ft
12 ft
40 ft
36 in
4
<
A
6 in
A
24 in
SECTION 1-1
2
I
8 in
D Homework 1
Problem 3 (25%)
The reinforced concrete column in the figure has a rectangular cross section. The column is subjected to 80
kips of axial compressive force at its top in addition to a uniform lateral load along the top 6 ft of the column
height. The unit weight of concrete is 150 pcf and the specified concrete strength, f'c is 3,000 psi. Do the
following:
(a) Draw the axial force and bending moment diagram of the column, show the bending moment in terms
of the lateral load w.
(b) If the lateral load is increased sufficiently to cause cracking in the column, where along the column is
the cracking most likely to occur? Draw the expected crack pattern.
(c) The lateral load w is increased until cracking occurs in the column. What is the value of the uniform
lateral load at which the column cracks? (Hint: Remember that the axial compressive force and column
self-weight increases the compressive stress in the column)
Uniform load, w (kip/ft)
16" x 20" column
20 in
3
80 kip
6 ft
12 ft Homework 1
Problem 4 (25%)
For each section below, assuming material properties f*c = 3,000 psi and Es = 29,000 ksi, compute the
following:
(a) The cracking moment using the gross moment of inertia of the section.
(b) The allowable moment using the transformed area method. Assume an allowable stress fs = 36,000 psi
and f' 1,200 psi for steel and concrete respectively.
=
C
9
4
3 in
24 in
36 in
8"
36
6 in
(5) #9
20 in
(C)
A
44
A
Δ
(4) #8
4
21 in
44
Δ
4
(6) #6
16 in
(A)
14 in
(B)
Δ
4
30 in
4
Δ
A
Δ
(3) # 10
12 in
(3) # 10
22 in
(D)
ง
A
A
14 in
3 in
2 in