# Design Problems with Solutions

Topics: Concrete, Shear stress, Reinforced concrete Pages: 55 (9601 words) Published: January 11, 2013
DESIGN PROBLEMS WITH SOLUTION

1. A propped beam having a span of 6m. carries a uniform load of 600kN/m. Which one of the following gives the reaction at B?

Solution:
Reaction at B:
-600(6)(3) = 10800
t B/A = 0
t B/A =

R = 1350

2. A 6 m. cantilever retaining wall, with an active pressure which varies from zero at the top of 35 kN/m at the bottom. Assume El is constant. Compute the maximum shear.

Solution:
Maximum shear:
Max. shear:

105 kN

3. The beam shown in the figure carries a triangular load which varies from 12 kN/m at A to 0 at B and a concentrated load of 20 kN at C. Which of the following gives the nearest value of the reaction at B? Solution:

38.67 kN

4. A truck with axle loads of 40 kN and 60 kN on a wheel base of 5 m. rolls across a 10 m. span. Which of the following gives the maximum bending moment?

Solution:
Maximum Bending moment:

Max. M =
Max. M = 40(4)
Max. M = 160 kN.m

5. A 12 mm thick steel tire, has a width of 110 mm and has an internal diameter of 800 mm. The tire is heated and shrunk to a steel wheel 800.5 mm diameter. Modulus of elasticity E = 200 GPa. Determine the tensile stress in the tire.

Solution:
Tensile stress in the tire:

mm

MPa
Tensile stress in the tire St = 125 MPa

6. From the continuous beam shown, it carries a uniform load from A to B and a concentrated load of 720 N at its mid span. Use moment distribution. Compute the fixed end moment due to the uniform load at A.

Solution:
Fixed end moment at A
(FEM)AB =
(FEM)AB =
(FEM)AB = -230.4 kN.m.

7. A rectangular beam has a width of 300 mm and an effective depth of 460 mm. The beam is reinforced with 2 – 28 mm ø at the top. fc’ = 35 MPa,fy = 350 MPa. Compute the balanced steel ratio of the reinforcement.

Solution:
Balanced steel ratio of the reinforcement.

= 0.043

8. A rectangular beam has a width of 300 mm and an effective depth of 460 mm. The beam is reinforced with 2 – 28 mm ø at the top. fc’ = 35 MPa,fy = 350 MPa. Compute the ratio of the depth of the compression block to the distance of the top fiber to the neutral axis. Solution:

Ratio of the depth of the compression block to the distance of the top fiber to the neutral axis. a = depth of compression block
c = distance of top fiber to neutral axis

a = ß C

ß =
ß = 0.85 – 0.008(fc’ - 30)
ß = 0.85 – 0.008(35 – 30)
ß = 0.81

9. A simply reinforced concrete beam has a width of 250 mm and an effective depth of 500 mm. Concrete strength is 28 MPa and steel yield strength Fy = 280 MPa. Which of the following gives the max. allowable steel area As in accordance with the 1992 NSCP strength design specifications.

Solution:
Balances steel ratio :
ß = 0.85 for fc’ < 30 MPa

= 0.0493
= 4.93%

10. The A-36 tension member is made up of an angular section 150 mm x 100 mm x 12.7 mm having a cross sectional area of 3060 mm2. It is connected with 3 – 19 mm ø bolts. Fu = 400 MPa,Fy = 248 MPa

Determine the tensile capacity of the member considering the gross area of the section.

Solution:
Tensile capacity based on gross area of section:
T = 0.60 Fy Ag
T = 0.60(248)(3060)
T = 455328 N
T = 455.3 kN

11. The section shows a double-angle tension for member BC, a web member in a light truss, having a length of 4 m. fasteners will be 19 mm ø A 325 bolts and will connect the double angle member to 9.5 mm gusset plate. Assuming that the strength of the gusset plate will not control. Fy = 250 MPa,Fu = 400 MPa.

Properties of 2 75 x 50 x 6 mm

Ag = 1535 mm2
ry = 22.63 mm
Determine the capacity of the member based on gross area.

Solution:
Capacity based on gross area:
T = 0.60 Fy Ag
T = 0.60(250)(1535)
T = 230250 N
T = 230.25 kN

12. From the given bracket shown, which consists of two plates riveted to the column by 4 – 22 mm ø rivets which is subjected to an eccentric load of 300 kN. Which of the following gives the shearing...