MECHANICAL STRUCTURES

Beams
 A beam is a supported bar that bears a load.
 Beams are used to construct structures such as houses, bridges, pylons, railway
lines, vehicles, furniture etc.
 Beams are made of various materials such as wood, metal, plastic, concrete and
stone.
Stress
 Stresses are internal forces set up in a loaded beam.
 Stress results from the weight of the beam and the load that it carries.
 There are three types of stress namely:
a) Tension (Tensile stress) – has a tendency of stretching an object.
Arrows used to show tension.
b) Compression (Compressive stress) – has a tendency of squeezing an object
Arrows used to show compression.
c) Shear – twists an object.

Types of beams
a) Simply supported beams: these are beams supported at both ends, in the
middle or along their length.
b) Cantilever beam: is a beam fixed at one end (e.g. in a wall) and loaded at the
free end).e.g. balcony and diving board.

LOADING A BEAM
 When a beam is loaded
a) Stresses are produced in it
b) It changes shape.

1. LOADING SIMPLY SUPPORTED BEAMS

(a). Beam supported at both ends and loaded in the middle

 Upper side of beam is under compression.

 Lower side of beam is under tension.
 Tensile strength is the ability of a beam to withstand tension (pulling forces).
 If the tension is greater than the tensile strength of the beam, cracks appear on
the lower side of the beam.

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(b). Beam supported at its centre and loaded at both ends is in tension on the
upper side and in compression on the lower side.

2. LOADING A CANTILEVER BEAM

(a). Cantilever beam is in tension on the upper side and in compression on the
lower side.

Experiment: Demonstrating compression and tension

Materials: Plastic ruler, glue, tissue paper, foam rubber cube, felt pen, two bricks.

METHOD 1
1. Laminate tissue paper on the lower and upper sides of a plastic ruler using glue.
2. Allow time for glue and tissue paper to dry and stick to the surfaces.
3. Load the beam (plastic ruler) such that it bends.
4. What do you observe?
Results

 On the upper side the tissue paper crinkles

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 At the bottom tissue paper tears

Explanation
There was compression at the top and tension at the bottom

METHOD 2
1) Draw parallel lines down a foam cube with a felt pen.
2) Load from above or push on it.
3) What do you observe?

Result

Explanation
The top of the beam is under compression (squeezed) and the bottom is under
tension.
The centre/middle of a beam, called the neutral axis (neutral layer or neutral zone),
is neither squeezed nor stretched. No stress acts in the neutral axis. The neutral axis
is not affected by any stress.

METHOD 3
Draw three parallel lines along a foam cube and load it from above.

RESULT

Explanation

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 Top of beam is under compression

 Middle of beam is not affected by stress. This is the neutral axis.
 The bottom of the beam is under compression.
NEUTRAL AXIS
 The neutral axis is a region in the beam where there is little or no stress. This
material is removed to make the beam lighter and to save material.
 Removing the neural axis results in beams with different cross-sectional shapes
and masses.
 The ratio of strength to mass of a beam is called strength- mass ratio. Lighter
beams have high strength mass ratio and are more useful.
 That is, a beam with the neutral axis removed has the following advantages over a
solid beam:
1. Higher strength to mass ratio.
2. Lighter
3. and therefore cheaper.
TYPES OF BEAMS
Beams are named using their cross sectional shape

The joining plates of I-beams, T-beams, Angle beams and Z-beams resist shear forces
while their flanges resist bending moments.
Name of beam Where used
Hollow box beam Wood constructions
Hollow cylindrical beam (Tube) For columns, increasing radius increases strength.
T- beam Bridges
I - beam In construction of railway lines, roof trusses, bridges
Angle beam Bridges, pylon trusses, roof trusses
Z- beam Bridges, wire poles

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FACTORS AFFECTING STRENGTH OF BEAMS

1. Type of material used.
 A beam must be made of stronger material to support a greater load. Most
beams are made of metal because metal has a high tensile strength.
2. Depth.
 Beams with greater depth are stronger e.g. a rectangular beam is stronger
when lying on edge because it has greater depth. The same beam easily
bends or breaks when lying flat because it has smaller depth.

3. Nature of load. Is the load tension, shear or compression.

4. For cylindrical beams diameter of the beam.
 Thicker beams can support more load.
 Increasing the thickness of a hollow cylindrical beam increases its strength
by preventing buckling and creasing.
5. Length of the beam.
Longer beams bend or surge easily because of increased self-load.
On a Beam bridge the span can be reduced by having many piers. This
prevents the deck from bending.
6. Weight of beam.
Beams used in structures must be light. If beams are too heavy the structure
will have too much weight to bear (carry) and therefore breaks or collapse
under its own weight.
7. Shape of beam.
 Some types of beams are more suitable for constructing certain
structures than others.
 Tubes (hollow cylindrical beams) are more common in engineering and
biological structures because they are equally strong in all directions at
right angles to their surface. Engineering structures such as bridges and
biological structures such as skeletal bones, bamboos and reeds are
composed of hollow cylindrical beams.
 Beams in tall structures are usually cylindrical in shape because under
compression cylindrical beams tend to crease rather than crack.

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EXPERIMENT: To test (determine) the strength of a beams.

Materials: Different types of beams of the same mass and made of the same
material, weights/masses, 2 clamp/retort stands
Method
1. Test each beam under load between two supports (see diagram below).
 For a fair comparison, use beams of the same material, mass, length and
diameter.
2. The load is increased gradually added until the beam breaks (fails).
3. Record your observations of exactly how, when and where the beam fails.

Results
Type of beam Mass that breaks the Force that breaks the
beam/kg beam/ Newtons
Hollow cylindrical beam 2.5 kg 25N
Solid cylindrical beam 2.4kg 24N
I-beam 2.2kg 22N
Angle beam 2.3kg 23N
T-beam 2.1kg 21N
Box beam 1.8kg 18N

Observations
The hollow cylindrical beam required the largest force to break it, followed by the
solid cylindrical beam, I-beam, angle beam, T-beam and finally the box beam.
Conclusion
 The strongest beam is the hollow cylindrical beam, followed by the solid
cylindrical beam, I-beam, angle beam, T-beam and lastly the box beam.
 The cross sectional shape of a beam determines its strength.

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TRUSSES
 A truss is a framework supporting a large structure e.g. roof, bridge, pylon, crane,
scaffolding etc.
 A truss is made up of two types of members namely struts and ties.
 A tie is a beam that must withstand tension. Ties can either be solid /hollow
beams or steel cables.
 A strut is a supporting beam that must withstand compression. Tubes, girders
and columns are examples of struts.
 A truss is composed of many connected members performing the function of a
beam.
 The members in a truss are connected to give a series of triangles. The more the
triangles the stronger and stable the truss.

Uses of trusses

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Trusses are used to support:

 Roofs
 Bridges
 Pylons
 Scaffoldings
 Cranes.
Advantages of trusses over beams
1) Good load distribution – made of many members which share stress.
2) Strong – made of many members, share load, have reduced self-load.
3) Light – their neutral axes are removed.
4) Economy (use less material) - some material was removed on their neutral axis.
5) Are stable – beams form a triangular shape.
EXPERIMENT: To show which members are under tension or compression in a
triangular truss.
Materials: rubber band, pins, two wooden beams
Method
1) Construct and load a triangular framework as shown below.

Result
1. The horizontal rubber band beam (lower beam) stretched. It was under tension.
2. The sloping rubber band beam buckled. It was under compression.
Conclusion
 The horizontal beam in a triangular truss is under tension. Therefore it is a tie.
It can be replaced by a cable, wire or chain which stay straight and tight when
under tension.
 The slanting side beams of a triangular truss are under compression. They
are struts. Solid or hollow beams are used for struts.

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ROOF TRUSS
 A roof truss is used to support the roof of a building.

TRUSSES IN LARGE STRUCTURES

Members parallel to this one are in compression

 The trellis (series of triangles) in a truss resists shear.

 The triangles give strength and stability to the structure.
 The more the triangles the stronger and more stable the structure.

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JOINING BEAMS
 A joint is a junction between beams.
 The function of a joint is to transmit load or stress from one part of a structure to
another.
 Stress is transmitted across a joint and, therefore, a joint need to be very strong.
Why are beams joined?
 To increase length.
 To allow for expansion.
 To allow transmission of stress between beams.
 Beams are joined to build a structure.

1. Pinning methods– use of screws, nails, rivets, bolts and nuts.

2. Surface contact methods – gluing, brazing, soldering, and welding.

(A). PINNING METHODS

1. PINNING METHODS OF JOINING WOOD

a) Nails (ordinary or gang nails)

 Used on permanent wood joints.
 Driven into wood with a hammer.
 Nails are made of metal e.g. iron.

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b) Screws
 Used on temporary or permanent wood joints.
 Driven in or taken out of wood using a screwdriver.
 Advantages of screws over nails
1. Screws are stronger, neater and more accurate.
2. Screws can be removed without damaging the wood.

c) Bolts and nuts

 Used permanently or temporarily to join large pieces of wood together.
 Used to join hard wood like mukwa, mahogany and teak.
 Spanners and sockets are used to fix bolts and nuts together.

2. PINNING METHODS OF JOINING METALS

a) Rivets
 A rivet is a metal fastener with a head attached to a shaft (shank or body) that
is passed through a hole in a material and flattened on the other side.
 Used to hold metal sheets/plates together.

 Two types of riveting are hot and cold.

 In hot riveting, holes are drilled through both sheets of metal. A hot rivet is
punched through the hole. The protruding end is hammered flat. As the rivet
cools it contracts pulling the sheets tightly together.

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 In cold riveting, a riveting tool punches holes in the metal sheets, inserts and
seals the rivets in one action.
 Cold riveting is used for thinner metal sheets and softer metals such as
aluminium.
 Disadvantages:
1. riveting is expensive
2. Riveting requires technical know-how.

b) Bolts and nuts

 Used permanently or temporarily to join metal beams.
 Spanners and sockets are used to tighten the bolts and nuts.
 A washer prevents the nut cutting into the metal as it is tightened.

STRENGTH OF PINNED JOINTS

 Pinning methods are used on lapped joints.
 A lapped joint is made of two overlapping ends of beams fastened together.
 The strength of a pinned joint depends on:
1. The area of overlap.
 The greater the area of overlap the stronger the joint
2. The number of pins (nails, screws or bolts and nuts) used.
 The more the pins used the stronger the joint.
 More pins share stress evenly.
 The pins in a lapped joint resist shear.
3. Position of pins
 If pins are very close to the edge of a joint, cracks easily develop along
the joint on loading it.
4. The material used to make the pins.
 Metal pins are stronger than plastic pins.
It takes a larger force to break a stronger joint than a weaker joint.

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(B). SURFACE CONTACT METHODS

1. SURFACE CONTACT METHODS OF JOINING WOOD

Gluing (with or without dowels and tongue and groove)

 Lapped joints and scarf joints in wood may be glued.
 Glue hardens to maintain the contact.

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The greater the area of overlap the stronger the glued joint is.
 Glued joints may further be strengthened by inserting pins (nails, screws) or
dowels across the joint.
 A dowel is a piece of wood used to join overlapping wooden beams by fitting
tightly into a hole drilled across them.
 The more the dowels the stronger the joint. Many dowels share stress.

2. SURFACE CONTACT METHODS OF JOINING METALS

a). Soldering
 Used for joining metal wires in electrical circuits and sealing tinplate joints.
 How soldering is done:
1. Solder (an alloy of tin and lead) has a low melting point.
2. The solder is melted using the hot tip of a soldering iron (soldering gun).
3. The molten solder then fuses metal wires or tin plates together as it cools.
b). Brazing
 Involves joining dissimilar metals with a molten brass metal rod.
 Brass (alloy of copper and zinc) is melted using gas.
 The molten brass solidifies to make a continuous joint.
 A braze joint is more flexible than a soldered joint.

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c). Welding
 Welding can be done using an electric arc or oxyacetylene.
 Welding is used to join similar metals unlike brazing which joins dissimilar metals.
Electric arc welding
 Involves joining similar iron/steel beams by melting a steel welding rod using heat
from an electric arc.
 The electric arc is produced by a small transformer called a welding machine.
 The molten steel solidifies and fuses the steel/iron beams together.
 Arc welding produces too much heat and intense light. Therefore, the following
safety precautions should be taken when welding:
1. Wear heat proof gloves for protection against heat.
2. Wear face mask with light filter for protecting eyes from intense light.

Oxyacetylene welding
 Oxyacetylene is a mixture of oxygen and acetylene gases.
 Burning the mixture of oxygen and acetylene provides heat to melt a rod that
fuses two similar metal beams.
 The heat from oxyacetylene is also used for cutting metal sheets.

ADVANTAGES OF RIVET JOINTS OVER WELDED JOINTS

1. A rivet joint stops cracks from spreading because of its discontinuity. Cracks
spread across a welded joint from one beam to the adjacent beam.
2. Rivet joints can slip a little to redistribute load so avoiding stress
concentrations. Slipping enables the rivets to share stress. Welded joints
often fail (crack) due to stress concentrations.
3. Rust fills the small gaps around rivets. The rust locks the joint and transmits
shearing forces equally between joined plates. On the contrary, rust may
corrode welded joints weakening the joint.

ADVANTAGES OF WELDED JOINTS OVER RIVET JOINTS

1. Welded joints are lighter than rivet joints.
2. Welded joints are cheaper than rivet joints.
3. Where streamlining is necessary, welded joints offer less resistance to air and
water.

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DISADVANTAGES OF WELDED JOINTS

a) It is difficult to obtain a perfect welded joint due to human error.
b) Due to its continuity, a welded joint does not stop cracks from spreading
across two adjacent metal beams.
3. SURFACE CONTACT METHODS OF JOINING PLASTICS
a) Gluing:
 Two overlapping plastic sheets can be glued together.
b) Welding
 Because plastic melts when heated, two plastic beams can fuse together
and form a strong joint. A filler rod of the same plastic can also be used if
necessary
PROPERTIES OF CONSTRUCTION MATERIALS

Materials for constructing large structures are chosen for good properties.
 Tough – crack resistant
 Strong – ability to withstand forces/stress.
 Stiff – does not give easily when hammered
 Brittle – can break easily
 Ductile – can be drawn into wire
 Malleable – can be hammered into different shapes without breaking.
 Porous – has pores and these can allow some substances to pass through.
 Light – low weight/ mass
 Flexible – bend without breaking.
 Durable – ability to resist decay and corrosion. Wood is durable if treated
against termites, wood borers and decay by microorganisms.
PROPERTIES OF TIMBER/WOOD
 Flexible
 Light
 Strong in tension when cut along grain
 Cheaper than steel
 Does not expand when heated unlike steel
Disadvantages of wood
1. Can catch fire
2. Can be attacked by wood borers, termites and microorganisms
Treatment of wood to increase durability
 Fireproofing using fire retardant
 Termite proofing using creosote
 Painting – to prevent it from absorbing moisture.
METALS AND ALLOYS
 Are ductile
 Are malleable – can be hammered into sheets, rods, bars and tubes.

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 Strong in tension and compression.

 Can be alloyed with other elements to change their properties.
Disadvantages of metals
1. Can be attacked by water and oxygen and acids
2. Metals are expensive
Treatment of metals to increase durability
 Electroplating
 Galvanising
 Painting
 Sacrificial protection using magnesium
CONCRETE
 Strong in compression
 Cheaper than steel
 Resistant to weather
 It can be moulded
 Can be reinforced to increase tensile strength
Disadvantages of concrete
1. Brittle – weak in tension
2. Heavier – than steel of the same strength
Reinforced concrete
 Strong in both tension and compression
 Cheaper than steel of the same strength
 Lighter than concrete of the same strength
 Can be moulded – precast or cast in situ.
 Resistant to weathering.
STONE
 Durable
 Strong in compression
Disadvantages of stone
1. Can be weathered
2. Inflexible
3. Difficult to shape
4. Heavy
ALUMINIUM
 Is light
 Does not corrode easily.

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BRIDGES
 Definition: A bridge is a beam/structure used for crossing a gap.
 The gap can be a river, a gorge/valley, a road or railway.
 A bridge spans a gap and enables people, animals and vehicles to get across the gap.
 A bridge in its simplest form consists of a bridge deck supported at both ends.
 Types of bridges
There are six main types of bridges:

 1. Pier and beam bridge (beam/girder bridge)  4. Truss bridge.

 2. Arch bridge  5. Cantilever bridge
 3. Suspension bridge.  6. Cable-stayed bridges.

This document shall look at the first four which are in the ZIMSEC science syllabus.

1. PIER AND BEAM BRIDGE also called Beam Bridge or Girder Bridge.

 Pier means a vertical supporting pillar/column. Piers prevent beam from bending.
 This bridge consists of a beam(s) supported at both ends by pillars (piers) or abutments.

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 The beams are made from concrete reinforced with steel rods. Concrete is strong under
compression and steel has high tensile strength.
 If the span is too long this bridge may have one or more supporting pillars along its length.
 The piers (pillars) or columns are under compression. Upper part of roadway beam is
under compression and the lower part is under tension.

2. ARCH BRIDGES
An arch bridge consists of a bridge deck (roadway) supported by an arch. The arch may be
above or below the bridge deck.
a) Through arch bridge (arch above bridge deck) e.g. Birchenough bridge over Save river.

 The function of the arch is to support a load by converting the downward force into sideways
thrust.
 The material for an arch should be strong in compression. Stone, concrete or steel is
therefore used.
 The arch is under compression.
 Suspending (supporting) beams are under tension. Therefore steel cables (ropes) are used
as suspending beams.
 Suspended roadway is free of compression and tension.

b). Arch below bridge deck e.g. Victoria Falls bridge over the Zambezi river.

 The arch is under compression.

 The supporting beams are under compression.
 Suspended roadway is free of compression and tension.
 Since the arch is under much compression, it needs very strong abutments to
provide the reaction force to the load. Therefore abutments must have very strong
foundations built on solid rock.
 The arch supports a load by converting the downward force into sideways thrust.

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c) Stone Arch Bridge

 Was used in ancient times
 The arch was also below the roadway.
 The arch is under compression.
 The load (downward force) pushes the stone units in the arch down and together.
This force runs down the ring of the arch and is transferred to the abutments.

Trussed arch
 A trussed arch is usually used in an arch bridge.
 A trussed arch is made of a triangulated (trellis) steel framework.
 The advantage of a trussed arch over a solid arch is that it reduces the weight of the
bridge and, therefore, decreases the force (thrust) on the abutments. This enables
engineers to build flatter arches with cheaper foundations.

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EXPERIMENT to demonstrate the strength of an arch

Materials: Two bricks, 5g plastic weights or coins, sheet of paper or thin manila sheet.
Method
1) Support a sheet of paper horizontally between two bricks as shown in diagram A.
2) Gradually load this horizontal beam with weights until it collapses. How much weight/
coins can it support before collapsing?
3) Arch the same sheet of paper between the two bricks as shown in diagram B. Load it
with weights until it collapses. How much weight/coins can it support before
collapsing?
4) Repeat the procedure with a flatter arch as shown in diagram C. How much
weight/coins can the flatter arch support before collapsing?

TYPICAL RESULTS

Structure Number of 5g weights it Load carried before

carries before collapsing collapsing/Newtons
A) Flat sheet 2 0.1N
B) Much curved arch 16 0.8N
C) Flatter arch 8 0.4N

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Conclusion
A much curved arch carries more load than either a flat beam or a flatter arch.
The Romans discovered the principle of the arch. A flat lintel of masonry
(stones/bricks) would collapse under its own weight.

 However, when the stones or bricks are made into an arch they can carry a
very large load.

 The load pushes the masonry down and together so that the arch is stable
and strong. The keystone is at the highest point of the arch. The key stone
locks other stones in place.
 The arch is much stronger when the load is applied from above.

3. SUSPENSION BRIDGE
3. SUSPENSION BRIDGE
 The Otto Beit Bridge over the Zambezi River at Chirundu is a suspension bridge.

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 The bridge deck (roadway) is suspended from an inverted arch.

 The Inverted arches avoid compression and use tension. Steel cables can
therefore be used because they are very strong in tension.
 Main cable, vertical cables and abutments are under tension.
 The pylons are under compression.
 Cables are made of steel. Steel is strong in tension.
 The abutments are under tension and therefore their foundations are
anchored on strong rock to prevent collapse of bridge.
 The vertical cables support the bridge deck and prevent it from bending.
 The triangulated truss below the deck:
a. Is composed of many members which share stress.
b. Has ties and struts (series of triangles) for rigidity and strength..
c. Has a high strength/mass ratio.
Materials used for constructing suspension bridges
 High tensile strength steel cables
 Steel trusses
 Reinforced concrete
Advantages of using steel cables
 Cables are light, so cheaper foundations can be constructed.
 Cables have no joint, are continuous therefore no area of weakness.
 Cables are very strong in tension.
 Wires share load if one fails the effect is not disastrous.

4. TRUSS BRIDGE

 A truss bridge is a bridge with triangular supports.

 The truss is a framework consisting of struts and ties.

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 Ties are beams which withstand tension. Ties can either be solid beams,
hollow beams or steel cables (ropes).
 Struts are supporting beams which withstand compression.

DAMS
 A dam is a structure constructed to hold huge volumes of water.
 Dams can be classified according to the building material used as earth dams or
concrete dams.
 There are two types of dam walls: earth dam wall and concrete dam wall.

1. Earth dam wall

 An earth dam is also called an embankment dam.
 An earth dam wall is used for shallower dams.
 Material for constructing earth dam wall: earth (soil) and rock (stone).
 The earth dam wall uses its weight to stand up to the force of water. When water
pushes against the earth dam wall, the heavy weight of the wall pushes down into
the ground and keeps the dam from falling over.
 Broad base withstands higher water pressure at the bottom.
 Compacted clay core is impervious. This makes the dam wall leak proof.
 Earth is cheap and locally available – it also increases stability of the wall.
 Slope of earth dam wall must not be greater than 30 O to avoid soil sliding down.
 Upstream side (side of dam wall facing the water) is covered with rock fill to
prevent erosion by waves and rain.
 Grass is planted on the downstream side to protect wall from erosion by rain.
 Large plants e.g. trees should not be planted on the dam wall as their roots cause
cracks in the wall so making it to leak.
 Top of dam wall must be higher than the maximum water level.
 Excess water must spill over a concrete spillway well below the height of the wall.

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 The spillway is made of concrete and not earth (soil) because concrete is not
easily eroded away.
 The spillway must be wider for faster spillage to prevent flooding.

 Question: Why is an earth dam wall wider at its base than a concrete dam wall?
 Answer: Clay is a weaker building material than concrete.

2. Concrete dam walls

 Two types of concrete dam walls are the arch (curved) concrete dam wall
and the straight concrete dam wall.
a) Arch (curved) concrete dam wall e.g. Kariba dam wall.
 The arch concrete dam wall is thin and used on wider rivers with large
amounts of water.
 The arch dam wall is built across a gorge (a deep narrow rocky valley).

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Features of an arch (curved) concrete dam wall

 Materials used for the curve concrete dam wall: reinforced concrete (concrete
and steel rods).
 Reinforced concrete is concrete embedded with steel rods to increase its
strength.
 Concrete is strong under compression.
 The steel rods are anchored in solid rock in the foundation.
 The steel rods are strong in tension, i.e. have high tensile strength, making
the wall and embankments strong under tension.
 The arch (curved) dam wall is under compression. The arch squeezes
together as water pushes against it.
 The arch transmits the thrust (force) from water pressure into the abutments.
 The arch is made convex (curved outwards) to the thrust of water.
 The curved wall has an increased surface area to reduce pressure on it.
 Foundations of the dam wall are built on solid rock to make the dam wall
stable and strong.

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PICTURE: Kariba Dam wall is an arch dam wall which is 24m wide and 579m high in some places

b) Straight concrete dam wall

 The straight concrete dam wall is used on narrow rivers and reservoirs.
Features of a straight concrete dam wall
 Materials used for the straight concrete dam wall: concrete and steel rods.
 Vertical steel rods in the dam wall are tensioned by means of a jacking device
above the wall. This increases the vertical force on the wall and acts like an
extra weight on top of the wall making it harder for the wall to move.
 Broad (wide) base of wall withstands higher water pressure at the bottom.
 By making the base of the wall wider, the centre of mass becomes lower. This
makes the dam wall more stable because the turning effect (moment) from
the water has been reduced.

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