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Analysis of Slabs

Concept Concept Concept Concept Concept Concept

Live Load Patterns

Concept Concept Concept

Shear and Moment Coefficients

Concept Concept Concept

Problem 1:

Design a one-way slab to carry a service live load of 12kN/m2 on a continuous span of 4m. Use f'c = 21MPa, fy = 275MPa, unit weight of concrete = 23.54kN/m3. Mu=wuL2/12 at supports and midspan.

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Problem 2:

The one-way slab has a thickness of 200 mm. It is reinforced with 25mmΦ bars spaced at 150mm on center. Clear covering is 18.75, fc'=20.7MPa, fy=276.5MPa, wt. of concrete = 24kN/m3. Span of slab is 3.6m center to center of support. Compute the service live load in kPa that the slab could carry assuming the only dead load is the weight of the slab. (Use NSCP 2010)

A. 47.48kPa
B. 34.78kPa
C. 40.58kPa
D. 41.34kPa

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Problem 3:

CE Board November 2021

Beam ABCD is to be analyzed for maximum forces at ultimate conditions.
The beam is simply supported at A, B, C, and D.
Service Loads:
DL=18kN/m
LL=11.5kN/m
1. Which of the following gives the maximum reaction at B?
2. Which of the following gives the maximum moment at B?
3. Which of the following gives the maximum shear at B?

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Problem 4:

CE Board May 2022

Beam ABCDE is to be analyzed for maximum forces at ultimate conditions.
The beam is simply supported at A, B, C, D, and E.
Factored Loads:
DL=15kN/m
LL=19kN/m
1. Determine the maximum shear at B.
2. Determine the maximum reaction at B.
3. Determine the maximum positive moment at span AB.

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Problem 5:

CE Board May 2022

At ultimate condition, the uniformly distributed loads for beams KLMNO and PQRST are as follows:
Dead Load, wDL=15kN/m (beam weight included)
Live Load, wLL=19kN/m
L=6m
s=2.5m
t=100mm
bxh=300mm450mm
For maximum stress, apply full live load.
Note: Use b=300mm as the column dimension parallel to the beam length

1. How much is the maximum negative moment in beam KLMNO?
2. Find the maximum shear in beam KLMNO.
3. What is the maximum positive moment in beam MN?

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Problem 6:

CE Board May 2022

Beam DEF is supported by spandrel beams at the exterior edges and by a column at E. The torsional resistance of beam ADG and CFI are not sufficient to restrain beam DEF at D and F.
For all beams, bxh = 300mmx450mm
For all column sections = 400mmx400mm
Dead Load, wuDL=6kN/m (beam weight included)
Live Load, wuLL=4.6kN/m
1. What is the critical negative moment at beam DEF?
2. Determine the critical positive moment at beam DEF.
3. Determine the critical shear force at beam DEF.

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Problem 7:

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Problem 8:

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