Prelim Activity #1: Principles of Reinforced/ Prestressed Concrete
Topic/s: Flexural Analysis of Beams
Learning outcome: For the students to be able to analyze beams under flexure.
Instruction/s: Solve the given problems completely in a separate sheet of clean paper and box your final
answer.
Problem # 1: A simply supported concrete rectangular beam has a cross-sectional dimension of 200mm
x 300mm and length L = (3 + N/5) m, is to be analyze in flexure, unit weight of the beam is 24kN/m^3.
Concrete properties: f’c = 28MPa, normal weight concrete, Es = 200000MPa
Calculate the following:
a. Weight of the beam in kN
b. Equivalent uniformly distributed load of the beams weight in kN/m.
c. Shear and Moment diagram of the beam due to self-weight, consider five points along its
length including points of support.
d. Maximum moment in the beam due to its own weight.
e. Moment of Inertia along x-axis
f. Moment of Inertia along y-axis
g. Moment of Inertia to resist bending due to vertical loads.
h. Maximum positive bending stress in the beam due to self-weight, in MPa
i. Maximum negative bending stress in the beam due to self- weight, in MPa
j. Location of maximum bending stress on the beam
Stress, in MPa
Point on the beam
Top or Bottom
k. Calculate the modulus of rupture for the concrete beam.
l. Calculate the cracking moment of the concrete beam.
m. Is the concrete beam uncracked, cracked or in the ultimate strength stage? Justify your
answer.
n. If concrete is uncracked, calculate the additional uniformly distributed load (in kN/m) on the
beam before it starts cracking.
o. If cracked, calculate the modular ratio.
Prepared by: Engr. Francis V. Villacorta