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Prof. Oral Buyukozturk Fall 2003
1.051 Structural Engineering Design
QUIZ 1
Open Book & Notes โ 90 minutes
QUESTION 1. โ FLEXURAL DESIGN (40%)
Consider a cantilever beam shown in the figure below which is loaded at its tip with a concentrated service dead load of PD=20 kips (including self-weight) and a service live load of PL=10 kips. The beam is 5 ft long and is anchored to one end of a column having 40 in width.
P D = 20 kips
P L = 10 kips
L=5 ft
b=14 in
h=20 in
40 in
A B
d
P D = 20 kips
P L = 10 kips
L=5 ft
b=14 in
h=20 in
40 in
A B
d
The effective depth of the beam is d=17.5 in. The material properties are: fc'^ = 4 ksi, fy= 60 ksi
(a) Under service loading, what is the nearest distance to the free end where you would start seeing flexural cracks? Consider only the gross area of concrete (neglect the steel when calculating the moment of inertia). The modulus of rupture of concrete is given by: fr=7.5 fc^ '
(b) Calculate the design load Pu and draw the shear and moment diagrams of the beam under design loads.
Prof. Oral Buyukozturk Fall 2003
(c) Determine the minimum and maximum reinforcement ratios for the beam. Briefly explain why we impose these limits.
(d) Assuming that the beam is underreinforced, determine the required reinforcement ratio, , and the corresponding reinforcement area, , in order for the beam to resist the design moment. Assume
r A s f = 0.9. After determining r , check if the beam is underreinforced.
(e) Perform the reinforcement design using #11 rebars and sketch your design.
(f) Using the provided reinforcement area, calculated in (e), determine the net tensile strain, e t , and check whether the assumption that f = 0.9 is valid.
QUESTION 2 โ SHEAR DESIGN (20%)
For the beam in Question 1,
(a) Calculate Vc using the simple expressions according to the ACI Code. In this case, does the location of the shear critical section bear any significance? Briefly explain.
(b) Determine if shear reinforcement is needed for this beam. If so, using the Vu and Vc previously calculated, determine the required shear reinforcement spacing using #3 stirrups. Would you make any changes in the stirrup spacing along the beam span?
Prof. Oral Buyukozturk Fall 2003
QUESTION 4 โ SERVICEABILITY AND STRENGTH DESIGN (15%)
(a) What do you understand from design for serviceability?
(b) With the aid of a sketch, explain how the beam shown in Question 1 may be affected by the creep of concrete. How will the strains and stresses at section A vary due to the creep of concrete?
