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Civil Problem Set 5

This document contains a civil engineering problem set with 8 questions involving the analysis of beams under different loading conditions to determine bending moments, shear forces, and maximum values. Questions involve calculating and sketching bending moment and shear force diagrams for determinate and indeterminate beams, as well as optimizing beam support locations.

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105 views3 pages

Civil Problem Set 5

This document contains a civil engineering problem set with 8 questions involving the analysis of beams under different loading conditions to determine bending moments, shear forces, and maximum values. Questions involve calculating and sketching bending moment and shear force diagrams for determinate and indeterminate beams, as well as optimizing beam support locations.

Uploaded by

Shrey
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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ENG1001 Civil Problem Set 5


1. Draw the deflected shape, the bending moment diagram and the shear force diagram for the
following beams (without calculations).

2. Calculate the bending moment at 2 metre intervals for the beam below, and plot the bending
moment diagram.

6 kN/m
20 kN
5m

10 m 10 m

3. Calculate the shear force at 2 metre intervals for the beam in question 2, and plot the shear
force diagram.

4. To determine how strong the beam below must be, it is necessary to know the maximum
values of the bending moment and the shear force. What are they?

10 kN 20 kN

5m 3m 2m
2

5. Sketch the deflected shape and draw shear force and bending moment diagrams for each
of the beams shown below. Note maximum values of shear and moment on the diagrams.

10 kN/m
a

10 m

10 kN/m
b

5m 5m

10 kN/m
c

5m

10 kN/m
d

5m 5m

10 kN/m
e

5m 5m

10 kN/m
f 10 kN

5m 5m

10 kN/m
10 kN
g

5m 5m
20 kN-m
3

6. The structural form of a flight of reinforced concrete stairs is represented by ABCDE


below, where DE is a landing cantilevered beyond the support at D. Assuming that the dead
load is 6 kN per metre run of stairs, obtain for this load the bending moments at A, B, C, D and
E, and also the shear force diagram for the part ABC.

1.5 m

D E

B C 2m

2m
A
1.5 m
300
7. The two span beam below is STATICALLY INDETERMINATE, but scales at B indicate that
the reaction there is 180 kN.
a) Obtain the shear force and bending moment diagrams.
b) Obtain the general mathematical expression for the bending moment between 0<x<8
c) Obtain the general mathematical expression for the bending moment between 8<x<11
d) Obtain the general mathematical expression for the bending moment between 11<x<16

20 kN/m 160 kN
C
204 kNm
A 8m B 3m 5m
x

Challenging Question:

8. The designer of the beam below intends to position the supports symmetrically so that the
maximum bending moment is as low as possible. Show that this is when, a   
2 1 L

w / unit length

a a
2L

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