CE Board Exam Randomizer

Singly-Reinforced Beams

Problem 1: Design of a Reinforced Concrete Beam

Design a reinforced concrete beam to carry a service dead load of 20kN/m (including its own weight) and service live load of 25kN/m plus a concentrated service live load of 30kN shown. Use f'c=21MPa, fy=276MPa, b=d/2, and ⌀=28mm main bars. The beam is to be reinforced in tension only.

See images:

Problem 2: Triangular Beam | Investigation Problem

For the beam shown below, f'c=27MPa, fy=270MPa, steel cover to centroid of bars = 100mm. A_s=4-32mm diameter bars.
a. Determine the depth of the compression block.
b. What is the compressive strength of concrete?
c. What is the nominal moment capacity of the beam?

See images:

Problem 3: Rectangular Beam | Investigation Problem

The beam shown is reinfoced with 3=28mm⌀ and its width is 300mm. The total height of the beam is 600mm. Assume that the clear cover is 40mm and 10mm⌀ stirrups are used. Use f'c=27.5MPa and fy=414MPa.
a. Compute the depth of the compression block in mm.
b. Determine the ultimate moment capacity of the beam section.
c. What additional service live load at the midspan can the beam carry in addition to a service dead load of 20kN/m (including its own weight)?

Beam Section and Ratio and Proportion based on strain converted to stresses:

Zoomed-in View of the computation of the centroidal cover:

Compute c and check fs if steel yields. If fs > fy, steel yields and we can proceed computing the nominal moment capacity. However, if fs < fy, we must recompute c and express C=T in terms of c.

Since steel yields, we keep the value of a and compute the nominal moment capacity by taking the couple moment: $Force\times Distance$. Note that C and T are equal in magnitude and opposite in direction, so they induce a couple moment equivalent to any one of the forces multiplied by the distance between them.

To compute the additional service live load at the midspan that the beam can carry in addition to a service dead load of 20kN/m, we first compute M_u since we must analyze beams at ultimate condition. To obtain M_u, simply multiply the nominal moment M_n by the reduction factor, Φ. Since fs exceeds 1000MPa, Φ=0.9 (tension-controlled). At ultimate condition, we also use the factored load combination: $1.2DL + 1.6LL$. Since the loadings are common, we can use the formulas: $\frac{PL}{4}$ and $\frac{w\cdot L^2}{8}$ for the maximum moments.

Problem 4: Rectangular Beam | Investigation Problem

A reinforced concrete beam with width of 300mm and d=410mm is reinforced for tension with a reinforcement area of 3700mm². Use f'c=27MPa and fy=415MPa.
a. Determine the distance (mm) of the steel reinforcements to the neutral axis.
A. 248
B. 162
C. 262
D. 148
b. Compute the tensile strain in the reinforcements.
A. 0.00196
B. 0.00169
C. 0.00122
D. 0.00244
c. If the beam is 8m long and is simply supported, find the concentrated service live load acting at the midspan that can be supported by the beam if it already carries a total service uniform dead load of 24kN/m.
A. 32.33
B. 52.32
C. 17.78
D. 66.13

See images:

Problem 5:

Refer to the image shown:

See images:

Problem 6:

Refer to the image shown:

See images:

Problem 7:

Refer to the image shown:

See images:

Problem 8:

Refer to the image shown:

See images: